{"id":4494,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/"},"modified":"2018-05-04T17:07:40","modified_gmt":"2018-05-04T11:37:40","slug":"ncert-solutions-class-12-maths-exercise-5-8","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 5.8"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Continuity_Differentiability\" >NCERT Solutions class 12\u00a0Continuity &amp; Differentiability\u00a0<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Maths_Exercise_58\" >NCERT Solutions class 12 Maths Exercise 5.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Maths_Exercise_58-2\" >NCERT Solutions class 12 Maths Exercise 5.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Maths_Exercise_58-3\" >NCERT Solutions class 12 Maths Exercise 5.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#5_Verify_Mean_Value_Theorem_if_in_the_interval_where_and_Find_all_for_which\" >5. Verify Mean Value Theorem if \u00a0in the interval \u00a0where \u00a0and \u00a0Find all \u00a0for which \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Maths_Exercise_58-4\" >NCERT Solutions class 12 Maths Exercise 5.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#6_Examine_the_applicability_of_Mean_Value_Theorem_for_all_the_three_functions_being_given_below\" >6. Examine the applicability of Mean Value Theorem for all the three functions being given below:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#NCERT_Solutions_class_12_Maths_Exercise_58-5\" >NCERT Solutions class 12 Maths Exercise 5.8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/#CBSE_App_for_Class_12\" >CBSE App for Class 12<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 5.8 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-continuity-and-differentiability\/1289\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Continuity and Differentiability\u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20pic.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 5.8\" width=\"189\" height=\"246\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Continuity_Differentiability\"><\/span>NCERT Solutions class 12\u00a0Continuity &amp; Differentiability<strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. Verify Rolle\u2019s theorem for <\/strong><strong><img decoding=\"async\" id=\"Picture 26\" style=\"height: 27px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image001.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Consider <img decoding=\"async\" id=\"Picture 41\" style=\"height: 27px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image002.png\" \/><\/p>\n<p><strong>(i) <\/strong>Function is continuous in <img decoding=\"async\" id=\"Picture 40\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image003.png\" \/>\u00a0as it is a polynomial function and polynomial function is always continuous.<\/p>\n<p><strong>(ii) <\/strong><img decoding=\"async\" id=\"Picture 39\" style=\"height: 27px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image004.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 38\" style=\"height: 27px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image005.png\" \/>\u00a0exists in <img decoding=\"async\" id=\"Picture 37\" style=\"height: 27px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image003.png\" \/>, hence derivable.<\/p>\n<p><strong>(iii) <\/strong><img decoding=\"async\" id=\"Picture 36\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image006.png\" \/>\u00a0and <img decoding=\"async\" id=\"Picture 35\" style=\"height: 27px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image007.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 34\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 33\" style=\"height: 27px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image009.png\" \/><\/p>\n<p>Conditions of Rolle\u2019s theorem are satisfied, hence there exists, at least one <img decoding=\"async\" id=\"Picture 32\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image010.png\" \/>\u00a0such that <img decoding=\"async\" id=\"Picture 31\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image011.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 29\" style=\"height: 19px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image013.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 28\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 27\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image014.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_58\"><\/span>NCERT Solutions class 12 Maths Exercise 5.8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>2. Examine if Rolles\/ theorem is applicable to any of the following functions. Can you say something about the converse of Rolle\u2019s theorem from these examples:<\/strong><\/p>\n<p><strong>(i) <\/strong><strong><img decoding=\"async\" id=\"Picture 25\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 24\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image016.png\" \/><\/strong><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(ii) <\/strong><strong><img decoding=\"async\" id=\"Picture 23\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 22\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image017.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p><strong>(iii) <\/strong><strong><img decoding=\"async\" id=\"Picture 21\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image018.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 20\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image019.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p><strong>Ans. (i) <\/strong>Being greatest integer function the given function is not differentiable and continuous<\/p>\n<p>hence Rolle\u2019s theorem is not applicable.<\/p>\n<p><strong>(ii) <\/strong>Being greatest integer function the given function is not differentiable and continuous hence Rolle\u2019s theorem is not applicable.<\/p>\n<p><strong>(iii)<\/strong> <img decoding=\"async\" id=\"Picture 47\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image018.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 46\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" id=\"Picture 45\" style=\"height: 29px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image020.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 44\" style=\"height: 29px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image021.png\" \/><img decoding=\"async\" id=\"Picture 43\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 42\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image022.png\" \/><\/p>\n<p>Hence, Rolle\u2019s theorem is not applicable.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_58-2\"><\/span>NCERT Solutions class 12 Maths Exercise 5.8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>3. If <\/strong><strong><img decoding=\"async\" id=\"Picture 19\" style=\"height: 27px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image023.png\" \/><\/strong><strong>\u00a0R is a differentiable function and if <\/strong><strong><img decoding=\"async\" id=\"Picture 18\" style=\"height: 27px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image005.png\" \/><\/strong><strong>\u00a0does not vanish anywhere, then prove that <\/strong><strong><img decoding=\"async\" id=\"Picture 17\" style=\"height: 27px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image024.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>For, Rolle\u2019s theorem, if<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong><img decoding=\"async\" id=\"Picture 58\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is continuous is <img decoding=\"async\" id=\"Picture 57\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" id=\"Picture 56\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is derivable in <img decoding=\"async\" id=\"Picture 55\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" id=\"Picture 54\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">Then, <img decoding=\"async\" id=\"Picture 53\" style=\"height: 27px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">It is given that <img decoding=\"async\" id=\"Picture 52\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is continuous and derivable, but <img decoding=\"async\" id=\"Picture 51\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 50\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 49\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 48\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 30\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image031.png\" \/><\/p>\n<hr \/>\n<p><strong>4. Verify Mean Value Theorem if <\/strong><strong><img decoding=\"async\" id=\"Picture 16\" style=\"height: 27px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image032.png\" \/><\/strong><strong>\u00a0in the interval <\/strong><strong><img decoding=\"async\" id=\"Picture 15\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image026.png\" \/><\/strong><strong>\u00a0where <\/strong><strong><img decoding=\"async\" id=\"Picture 14\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image033.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" id=\"Picture 13\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image034.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Function is continuous in [1, 4] as it is a polynomial function and polynomial function is always continuous.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong><img decoding=\"async\" id=\"Picture 68\" style=\"height: 27px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image035.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 67\" style=\"height: 27px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image005.png\" \/>\u00a0exists in [1, 4], hence derivable. Conditions of MVT theorem are satisfied, hence there exists, at least one <img decoding=\"async\" id=\"Picture 66\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image036.png\" \/>\u00a0such that<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 65\" style=\"height: 44px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 64\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 63\" style=\"height: 44px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 62\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 61\" style=\"height: 19px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 60\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 59\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image040.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_58-3\"><\/span>NCERT Solutions class 12 Maths Exercise 5.8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"5_Verify_Mean_Value_Theorem_if_in_the_interval_where_and_Find_all_for_which\"><\/span><strong>5. Verify Mean Value Theorem if <\/strong><strong><img decoding=\"async\" id=\"Picture 12\" style=\"height: 27px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image041.png\" \/><\/strong><strong>\u00a0in the interval <\/strong><strong><img decoding=\"async\" id=\"Picture 11\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image026.png\" \/><\/strong><strong>\u00a0where <\/strong><strong><img decoding=\"async\" id=\"Picture 10\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image033.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" id=\"Picture 9\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image042.png\" \/><\/strong><strong>\u00a0Find all <\/strong><strong><img decoding=\"async\" id=\"Picture 8\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image043.png\" \/><\/strong><strong>\u00a0for which <\/strong><strong><img decoding=\"async\" id=\"Picture 7\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image044.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>Function is continuous in [1, 3] as it is a polynomial function and polynomial function is always continuous.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong><img decoding=\"async\" id=\"Picture 101\" style=\"height: 27px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image045.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 100\" style=\"height: 27px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image005.png\" \/>\u00a0exists in [1, 3], hence derivable. Conditions of MVT theorem are satisfied, hence there exists, at least one <img decoding=\"async\" id=\"Picture 99\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image043.png\" \/>\u00a0such that<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 98\" style=\"height: 44px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 97\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 96\" style=\"height: 44px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 95\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 94\" style=\"height: 21px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 93\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 92\" style=\"height: 21px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 91\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 89\" style=\"height: 21px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 88\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 87\" style=\"height: 27px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 86\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 85\" style=\"height: 27px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 84\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 83\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image053.png\" \/>\u00a0or <img decoding=\"async\" id=\"Picture 82\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 81\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 80\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image055.png\" \/>\u00a0or <img decoding=\"async\" id=\"Picture 79\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 78\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 77\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image057.png\" \/>\u00a0or <img decoding=\"async\" id=\"Picture 76\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 75\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 74\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image057.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 73\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image058.png\" \/>\u00a0and other value <img decoding=\"async\" id=\"Picture 72\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since <img decoding=\"async\" id=\"Picture 71\" style=\"height: 27px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image059.png\" \/>, therefore the value of <img decoding=\"async\" id=\"Picture 70\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image060.png\" \/>\u00a0does not exist such that <img decoding=\"async\" id=\"Picture 69\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image061.png\" \/>.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_58-4\"><\/span>NCERT Solutions class 12 Maths Exercise 5.8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"6_Examine_the_applicability_of_Mean_Value_Theorem_for_all_the_three_functions_being_given_below\"><\/span><strong>6. Examine the applicability of Mean Value Theorem for all the three functions being given below:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>(i) <\/strong><strong><img decoding=\"async\" id=\"Picture 6\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 5\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image016.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p><strong>(ii) <\/strong><strong><img decoding=\"async\" id=\"Picture 4\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 3\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image017.png\" \/><\/strong><\/p>\n<p><strong>(iii) <\/strong><strong><img decoding=\"async\" id=\"Picture 2\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image018.png\" \/><\/strong><strong>\u00a0for <\/strong><strong><img decoding=\"async\" id=\"Picture 1\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image019.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Mean Value Theorem states that for a function <img decoding=\"async\" id=\"Picture 159\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image062.png\" \/>\u00a0R, if<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> <img decoding=\"async\" id=\"Picture 158\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is continuous on <img decoding=\"async\" id=\"Picture 157\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong><img decoding=\"async\" id=\"Picture 156\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is differentiable on <img decoding=\"async\" id=\"Picture 155\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">Then there exist some <img decoding=\"async\" id=\"Picture 154\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image064.png\" \/>\u00a0such that <img decoding=\"async\" id=\"Picture 153\" style=\"height: 44px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, the Mean Value Theorem is not applicable to those functions that do not satisfy any of the two conditions of the hypothesis.<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> <img decoding=\"async\" id=\"Picture 152\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/>\u00a0for <img decoding=\"async\" id=\"Picture 151\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\">It is evident that the given function <img decoding=\"async\" id=\"Picture 150\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is not continuous at <img decoding=\"async\" id=\"Picture 149\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image067.png\" \/>\u00a0and <img decoding=\"async\" id=\"Picture 148\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image068.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 147\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is not continuous at <img decoding=\"async\" id=\"Picture 146\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image069.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now let <img decoding=\"async\" id=\"Picture 145\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image070.png\" \/>\u00a0be an integer such that <img decoding=\"async\" id=\"Picture 144\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 143\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0L.H.L. = <img decoding=\"async\" id=\"Picture 142\" style=\"height: 44px; width: 444px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image072.png\" \/><\/p>\n<p style=\"text-align: justify;\">And R.H.L. = <img decoding=\"async\" id=\"Picture 141\" style=\"height: 44px; width: 411px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image073.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since,\u00a0 L.H.L. <img decoding=\"async\" id=\"Picture 140\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image074.png\" \/>\u00a0R.H.L.,<\/p>\n<p style=\"text-align: justify;\">Therefore <img decoding=\"async\" id=\"Picture 139\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is not differentiable at <img decoding=\"async\" id=\"Picture 138\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image069.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence Mean Value Theorem is not applicable for <img decoding=\"async\" id=\"Picture 137\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/>\u00a0for <img decoding=\"async\" id=\"Picture 136\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong><img decoding=\"async\" id=\"Picture 135\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/>\u00a0for <img decoding=\"async\" id=\"Picture 134\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\">It is evident that the given function <img decoding=\"async\" id=\"Picture 133\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is not continuous at <img decoding=\"async\" id=\"Picture 132\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image075.png\" \/>\u00a0and <img decoding=\"async\" id=\"Picture 131\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 130\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is not continuous at <img decoding=\"async\" id=\"Picture 129\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now let <img decoding=\"async\" id=\"Picture 128\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image070.png\" \/>\u00a0be an integer such that <img decoding=\"async\" id=\"Picture 127\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image078.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 126\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0L.H.L. = <img decoding=\"async\" id=\"Picture 125\" style=\"height: 44px; width: 444px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image072.png\" \/><\/p>\n<p style=\"text-align: justify;\">And R.H.L. = <img decoding=\"async\" id=\"Picture 124\" style=\"height: 44px; width: 411px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image073.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since,\u00a0 L.H.L. <img decoding=\"async\" id=\"Picture 123\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image074.png\" \/>\u00a0R.H.L.,<\/p>\n<p style=\"text-align: justify;\">Therefore <img decoding=\"async\" id=\"Picture 122\" style=\"height: 21px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image025.png\" \/>\u00a0is not differentiable at <img decoding=\"async\" id=\"Picture 121\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence Mean Value Theorem is not applicable for <img decoding=\"async\" id=\"Picture 120\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image015.png\" \/>\u00a0for <img decoding=\"async\" id=\"Picture 119\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong><img decoding=\"async\" id=\"Picture 118\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image018.png\" \/>\u00a0for <img decoding=\"async\" id=\"Picture 117\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image019.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Here, <img decoding=\"async\" id=\"Picture 116\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is a polynomial function of degree 2.<\/p>\n<p style=\"text-align: justify;\">Therefore, <img decoding=\"async\" id=\"Picture 115\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is continuous and derivable everywhere i.e., on the real time <img decoding=\"async\" id=\"Picture 114\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence <img decoding=\"async\" id=\"Picture 113\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image066.png\" \/>\u00a0is continuous in the closed interval [1, 2] and derivable in open interval (1, 2).<\/p>\n<p style=\"text-align: justify;\">Therefore, both conditions of Mean Value Theorem are satisfied.<\/p>\n<p style=\"text-align: justify;\">Now, From eq. (i), <img decoding=\"async\" id=\"Picture 112\" style=\"height: 27px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 111\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 110\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image081.png\" \/><\/p>\n<p style=\"text-align: justify;\">Again,\u00a0 From eq. (i), <img decoding=\"async\" id=\"Picture 109\" style=\"height: 29px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image082.png\" \/><\/p>\n<p style=\"text-align: justify;\">And From eq. (ii), <img decoding=\"async\" id=\"Picture 108\" style=\"height: 29px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 107\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image008.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 106\" style=\"height: 44px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image084.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 105\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 104\" style=\"height: 41px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image085.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 103\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image012.png\" \/>\u00a0<img decoding=\"async\" id=\"Picture 102\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex5.8\/image086.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Mean Value Theorem is verified.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_58-5\"><\/span>NCERT Solutions class 12 Maths Exercise 5.8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Class_12\"><\/span>CBSE App for Class 12<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 5.8 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 5.8\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-5-8\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 5.8\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4494","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 5.8 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 5.8 in PDF format for free download. 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