Mathematics - Continuity - Differentiability Question with Solution | TestHub

Given function is $f\left(x\right)=\left\{\begin{array}{cc}max\left(\left|x\right|, x^2\right),& \left|x\right|\le 2\\ 8-2\left|x\right|,& 2<\left|x\right|\le 4\end{array}\right.$

The graph of the function, is

We know that, a function is not differentiable at a point where its graph has a sharp corner.

And, from the graph we can easily conclude that $f\left(x\right)$ is non-derivable at $x=-2, -1, 0,1, 2$

Hence, the set $S=\left\{-2, -1, 0,1, 2\right\}.$