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Let f(x)={(x-1)sin1/(x-1)if\ x!=1 0,\ if...

Let `f(x)={(x-1)sin1/(x-1)if\ x!=1 0,\ if\ x=1` . Then which one of the following is true? `f` is differentiable at `x=0\ ` and at`\ x-1` `f` is differentiable at `x=0\ ` but not at`\ x=1` `f` is differentiable at `x=0` nor at `x=1` `f` is differentiable at `x=1\ ` but not at`\ x=0`

A

f is differentiable at x = 1 but not at x = 0

B

f is neither differentiable at x = 0 nor at x = 1

C

f is differentiable at x = 0 and at x = 1

D

f is differentiable at x = 0 but not at x = 1

Text Solution

Verified by Experts

The correct Answer is:
D
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