### myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Install NowNCERT 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.

**Download NCERT solutions for Continuity and Differentiability as PDF.**

## NCERT Solutions class 12 Continuity & Differentiability** **

**1. Verify Rolle’s theorem for **** **

**Ans. **Consider

**(i) **Function is continuous in as it is a polynomial function and polynomial function is always continuous.

**(ii) ** exists in , hence derivable.

**(iii) ** and

Conditions of Rolle’s theorem are satisfied, hence there exists, at least one such that

### NCERT Solutions class 12 Maths Exercise 5.8

**2. Examine if Rolles/ theorem is applicable to any of the following functions. Can you say something about the converse of Rolle’s theorem from these examples:**

**(i) **** for **** **

**(ii) **** for **** **

**(iii) **** for **** **

**Ans. (i) **Being greatest integer function the given function is not differentiable and continuous

hence Rolle’s theorem is not applicable.

**(ii) **Being greatest integer function the given function is not differentiable and continuous hence Rolle’s theorem is not applicable.

**(iii)**

Hence, Rolle’s theorem is not applicable.

### NCERT Solutions class 12 Maths Exercise 5.8

**3. If **** R is a differentiable function and if **** does not vanish anywhere, then prove that **** **

**Ans. **For, Rolle’s theorem, if

**(i) ** is continuous is

**(ii)** is derivable in

**(iii)**

Then,

It is given that is continuous and derivable, but

**4. Verify Mean Value Theorem if **** in the interval **** where **** and **** **

**Ans. (i)** Function is continuous in [1, 4] as it is a polynomial function and polynomial function is always continuous.

**(ii) ** exists in [1, 4], hence derivable. Conditions of MVT theorem are satisfied, hence there exists, at least one such that

### NCERT Solutions class 12 Maths Exercise 5.8

**5. Verify Mean Value Theorem if **** in the interval **** where **** and **** Find all **** for which **** **

**Ans. (i) **Function is continuous in [1, 3] as it is a polynomial function and polynomial function is always continuous.

**(ii) ** exists in [1, 3], hence derivable. Conditions of MVT theorem are satisfied, hence there exists, at least one such that

or

or

or

and other value

Since , therefore the value of does not exist such that .

### NCERT Solutions class 12 Maths Exercise 5.8

**6. Examine the applicability of Mean Value Theorem for all the three functions being given below:**

**(i) **** for **** **

**(ii) **** for **

**(iii) **** for **** **

**Ans. **Mean Value Theorem states that for a function R, if

**(i)** is continuous on

**(ii) ** is differentiable on

Then there exist some such that

Therefore, the Mean Value Theorem is not applicable to those functions that do not satisfy any of the two conditions of the hypothesis.

**(i)** for

It is evident that the given function is not continuous at and

Therefore,

is not continuous at

Now let be an integer such that

L.H.L. =

And R.H.L. =

Since, L.H.L. R.H.L.,

Therefore is not differentiable at

Hence Mean Value Theorem is not applicable for for

**(ii) ** for

It is evident that the given function is not continuous at and

Therefore,

is not continuous at

Now let be an integer such that

L.H.L. =

And R.H.L. =

Since, L.H.L. R.H.L.,

Therefore is not differentiable at

Hence Mean Value Theorem is not applicable for for

**(iii) ** for ……….(i)

Here, is a polynomial function of degree 2.

Therefore, is continuous and derivable everywhere i.e., on the real time

Hence is continuous in the closed interval [1, 2] and derivable in open interval (1, 2).

Therefore, both conditions of Mean Value Theorem are satisfied.

Now, From eq. (i),

Again, From eq. (i),

And From eq. (ii),

Therefore, Mean Value Theorem is verified.

## NCERT Solutions class 12 Maths Exercise 5.8

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

## CBSE App for Class 12

To download NCERT 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 **the best app for CBSE students** and myCBSEguide website.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Create NowmyCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Install Now
solution for answer number 5 is wrong. The diff. of f(x) is given wrong, a -3 is missing there. It should have been, f(x)= 3x^2 – 10x – 3, rather than f(x)= 3x^2 – 10x.

Class 12 NCERT Ex 5.8 Question no. 5 is incorrect

f'(3)=-27 not -21

NCERT solutions is best solutions

Thanks for all the help!!

5th sum in EX 5.8 IS WRONG PLS CORRECT IT

Ncert is the best I love u Ncert…. Love u muhh

Thanks for help me