## C(1) Function

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### Proof:

We have studied this function before. The details are left as an exercise, but here is the idea:

*g*is differentiable for all non-zero*x*(apply some theorems)- find the derivative for non-zero
*x*by using chain and product rules - find the derivative of
*g*at zero by looking at the limit of the difference quotient at zero - show that the derivative you have just found is not continuous
at zero by considering left and right limits as
*x*approaches zero