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Suppose that f (x) is a differentiable f...

Suppose that `f (x)` is a differentiable function such that `f'(x)` is continuous, `f'(0)=1 and f''(0)` does not exist. Let `g(x)= xf '(x)`, Then

A

`g'(0)` does not exist

B

`g'(0) =0`

C

`g '(0) =1`

D

`g'(0) =2`

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The correct Answer is:
C
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