Question

find the absolute maximum of f on -8,9.
select the correct choice below and, if necessary, fill in the answer boxes to complete your choice
a. the absolute maximum of f is f(\\(\square\\)) = \\(\square\\)
(type integers or fractions.)
b. there is no absolute maximum

Explanation:

Step1: Identify interval critical points

The interval is $[-8,9]$. We check all peak points and endpoints on the graph within this range.

Step2: Compare function values

• At $x=-8$: $f(-8)=0$
• At $x=-5$: $f(-5)=6$ (the highest peak)
• At $x=0$: $f(0)=0$
• At $x=2$: $f(2)=2$
• At $x=4$: $f(4)=-8$
• At $x=7$: $f(7)=2$
• At $x=9$: $f(9)=0$

The largest value is 6 at $x=-5$.

Answer:

A. The absolute maximum of $f$ is $f(-5)=6$