At how many points is $f(x) = x\lvert x \rvert$ not differentiable?

Explanation

1. 01

   $f(x) = -x^{2}$ for $x < 0$ and $x^{2}$ for $x \ge 0$.

2. 02

   Both slopes are 0 at 0, so it is differentiable everywhere: 0 points.