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

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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