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# NCERT Solutions class 12 Maths Exercise 5.8

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## 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

### 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 .

### 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

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### 7 thoughts on “NCERT Solutions class 12 Maths Exercise 5.8”

1. 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.

2. Class 12 NCERT Ex 5.8 Question no. 5 is incorrect
f'(3)=-27 not -21

3. NCERT solutions is best solutions

4. Thanks for all the help!!

5. 5th sum in EX 5.8 IS WRONG PLS CORRECT IT

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

7. Thanks for help me