Question

Let $f(x) = (x + 3)^2 (x - 2)^3$, $x \in [-4, 4]$. If $M$ and $m$ are the maximum and minimum values of $f$, respectively in $[-4, 4]$, then the value of $M - m$ is:

• A. 600
• B. 392
• C. 608
• D. 108

Answer 1

Answer: (C)

608

Answer 2

To find the maximum and minimum values of $f(x)$:

Take the derivative $f'(x)$ and find the critical points.

Evaluate $f(x)$ at critical points and endpoints $x = -4, -3, -2, -1, 1, 2, 3, 4$.

The maximum value $M = 392$ and the minimum value $m = -216$.

The value of $M - m$ is:

$M - m = 392 - (-216) = 608.$