NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 22 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 69:

.

Answer:

We have,

(i) is continuous function.

[Since every polynomial function is a continuous function]

Hence, is continuous in

(ii)

which exists everywhere except at

Hence, is continuous in

(iii)

Conditions of Rolle՚s theorem are satisfied.

Hence, there exists a real number c such that

Hence, Rolle՚s theorem has been verified.

Question 70:

Discuss the applicability of Rolle՚s theorem on the function given by

Answer:

Given:

First of all, Conditions of Rolle՚s theorem are:

(a) is continuous at

(b) is derivable at

(c)

If all three conditions are satisfied then there exist some in such that

Condition 1:

At

and

Hence, condition is satisfied.

Condition 2:

Now, we have to check is differentiable

On differentiating with respect to , we get

Or

Now, let us consider the differentiability of

is not differentiable at

Thus, Rolle՚s Theorem is not applicable to the given function.