Respuesta
If $f'(c) = 0$ and $f''(c) > 0$, $f(c)$ is a local minimum; if $f'(c) = 0$ and $f''(c) < 0$, $f(c)$ is a local maximum.
Explicación
If $f''(c) = 0$, the test is inconclusive and higher derivatives or sign changes of $f'(x)$ must be examined.