question_answer

Let \[f(x)=\left\{ \begin{matrix}    0, & x<0  \\    {{x}^{2}} & x\ge 0  \\ \end{matrix} \right.,\] then for all values of x

A)  \[f\]is continuous but not differentiable

B)  \[f\] is differentiable but not continuous

C)  \[f'\]is continuous but not differentiable

D)  \[f'\]is continuous and differentiable

E)  None of these