Let $f:R \to R$ be differentiable at $c \in R$ and $f(c) = 0.$ If $g(x) = \left| {f(x)} \right|,$ then at $x = c,$ $g$ is

Differentiable if $f'(c) \ne 0$

Not differentiable if $f'(c) = 0$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f:R \to R

be differentiable at

c \in R

and

f(c) = 0.

g(x) = \left| {f(x)} \right|,

then at

x = c,

g

View answer and explanation

Correct option: D

Differentiable if

f'(c) = 0

Option D (Differentiable if

f'(c) = 0

) is correct because if

f'(c) = 0

, then the limit defining

g'(c)

exists and is equal to 0, making

g

differentiable.

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