Answer
$18 \leq f(8) - f(2) \leq 30$
Work Step by Step
Using the Mean Value Theorem, we have:
$f'(c) = \frac{f(8) - f(2)}{8 - 2}$
$f'(c) = \frac{f(8) - f(2)}{6}$
$3 \leq f'(c) \leq 5$
$3 \leq \frac{f(8) - f(2)}{6} \leq 5$
Multiply each side by $6$:
$(6)3 \leq (6) \frac{f(8) - f(2)}{6} \leq 5 (6)$
$(6)3 \leq f(8) - f(2) \leq 5 (6)$
$18 \leq f(8) - f(2) \leq 30$