For a twice-differentiable $f$, $f'(2) = 0$ and $f''(2) = -3$. What does the second derivative test say about $x = 2$?

Explanation

1. 01

   $f'' < 0$ at a critical point means a local maximum, $f'' > 0$ a local minimum.

2. 02

   Here $f''(2) = -3$, so it is a local maximum.