Which of these describes $f(x) = x\lvert x \rvert$ at $x = 0$?

Explanation

1. 01

   $f(x) = -x^{2}$ for $x < 0$ and $x^{2}$ for $x \ge 0$; both pieces give 0 at 0.

2. 02

   Both one-sided derivatives are 0: differentiable.