What are the left-hand and right-hand derivatives of $f(x) = \lvert x^{2} - 4 \rvert$ at $x = 2$?

Explanation

1. 01

   Just left of 2, $x^{2} - 4 < 0$, so $f = 4 - x^{2}$ with slope $-2x = -4$.

2. 02

   Just right of 2, $f = x^{2} - 4$ with slope $2x = 4$.