Question

If $f\left(x\right)=\{\begin{array}{cc}\text{min}\{x,x^2\},& x\ge 0\\ \text{min}\{2x,x^2-1\},& x<0\end{array}$ then the number of points where $f\left(x\right)$ is non-differentiable in $[-2,2]$ is

Answer 1

$f\left(x\right)=\{\begin{array}{cc}x,& x>1\\ x^2,& 0\le x\le 1\\ x^2-1,& 1-\sqrt{2}\le x<0\\ 2x,& x<1-\sqrt{2}\end{array}$
So $f\left(x\right)$ is not differentiable at $x=1-\sqrt{2},0,1.$