If $f'(c) = 0$ and $f''(c) < 0$, which of the following must be true about the function $f$ at $x = c$?

Core Concept

Correct. The Second Derivative Test states that if $f'(c) = 0$ and $f''(c) < 0$, then $f$ has a relative maximum at $x = c$ because the graph is concave down at this critical point.