Let $f(x) = x^3 - 3x^2 - 9x + 5$ on the closed interval $[-2, 4]$. What is the absolute maximum value of $f$ on this interval?

Core Concept

Correct. By the Candidates Test, the absolute maximum must occur at a critical point or an endpoint. The derivative $f'(x) = 3(x-3)(x+1)$ yields critical points at $x=3$ and $x=-1$. Evaluating $f$ at all candidates gives $f(-2) = 3$, $f(-1) = 10$, $f(3) = -22$, and $f(4) = -15$. The largest value is 10.