question_answer

Let \[f(x)=\left\{ \begin{matrix}    \max \left\{ \left| x \right|,{{x}^{2}} \right\} & \left| x \right|\le 2  \\    8-2\left| x \right| & 2<\left| x \right|\le 4  \\ \end{matrix}. \right.\] Let S be the set of points in the interval \[(-4,4)\] at which differentiable. Then S:

A) is an empty set  

B)  equals \[\left\{ -2,-1,\,\,1,\,\,2 \right\}\]

C) equals \[\left\{ -2,-1,\,\,1,\,\,2 \right\}\]

D) equals \[\left\{ -2,\,\,2 \right\}\]