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

The Correct Option is C

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:

\[ M - m = 392 - (-216) = 608. \]