Q .     Let `f(x) = {( (x - 1)sin(1/(x-1)), if x!= 1), (0, if x = 1):}`. Then which one of the following is true?

JEE 2008
A

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

B

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

C

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

D

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

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