Let , then for all values of | CGP Edu

Maths Functions, Limits, Continuity and Differentiability Differentiability Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

Let , then for all values of

A

f is continuous but not differentiable

B

f is differentiable but not continuous

C

is continuous but not differentiable

D

is continuous and differentiable

Text Solution

Verified by Experts

The correct answer is:

;

and

⇒ ⇒

Hence is continuous function at .

⇒ ⇒

Hence is differentiable at .

Now ;

and

⇒ ⇒

Hence is continuous function at .

Now

⇒ ⇒

Hence is not differentiable at .

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