Which of the following functions is differentiable at x = 0? | CGP Edu

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Which of the following functions is differentiable at x = 0?

A

cos (|x|) + |x|

B

cos (|x|) − − |x|

C

sin (|x|) + |x|

D

sin (|x|) − − |x|

Text Solution

Verified by Experts

The correct answer is:

f(x) = cos |x| + |x| =

f’(x) =

∴ ∴ Not differentiable

f(x) cos |x| − − |x| =

Not differentiable at x = 0

f(x) sin |x| + |x| =

Not differentiable at x = 0

f(x) = sin|x| − − |x| =

f’(x) =

∴ ∴ f is differentiable at x = 0.

∴ ∴ D is correct alternative.

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