Let f(x)=cases|x|,x^2, & |x|28-2|x|, & 2

Question

Let $f(x)=\begin{cases}\max\{|x|,x^2\}, & |x|\le2\8-2|x|, & 2<|x|\le4\end{cases}$. Let $S$ be the set of points in the interval $(-4,4)$ at which $f$ is not differentiable. Then $S$:

Accepted Answer

$f$ is non-differentiable at the corners: $x=0$ (from $|x|$), $x=\pm1$ (where $|x|=x^2$), and $x=\pm2$ (join between the two pieces). So $S=\{-2,-1,0,1,2\}$.

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