If f (x) is differentiable everywhere, then :

Maths Functions, Limits, Continuity and Differentiability Derivability at a Point and in an Interval Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

⏐ f ⏐ is differentiable everywhere

is differentiable everywhere

f ⏐ f ⏐ is not differentiable at some point

f + ⏐ f ⏐ is differentiable everywhere

Text Solution

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The correct answer is:

If ' f ' is differentiable

then |f| is differentiable at each point x, where f(x) ≠ 0

if f( α ) = 0 and f ′ ( α ) = 0, then |f| is differentiable at x = α

if f( α ) = 0 and f ′ ( α ) ≠ 0, then |f| is not differentiable at x = α

⇒ If f is differentiable then |f| may or may not be

differentiable, [option A, C, D not necessarly true]

Now |f| 2 = f 2

(f 2 ) ′ = 2.f.f ′ since f is differentiable

∴ f 2 is also differentiable

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