Question

by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.
g(x)=x² - 2 on -5,4
find the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice
the absolute minimum is -2 at x = 0
(use a comma to separate answers as needed )
there is no absolute minimum
find the absolute maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice
the absolute maximum is at x =
(use a comma to separate answers as needed )
there is no absolute maximum

Explanation:

Step1: Analyze the function \(g(x)=x^{2}-2\)

This is a parabola opening upwards (\(a = 1>0\) in \(y = ax^{2}+bx + c\)) with vertex at \((0,-2)\).

Step2: Evaluate the function at the endpoints of the interval \([-5,4]\)

• When \(x=-5\), \(g(-5)=(-5)^{2}-2=25 - 2=23\).
• When \(x = 4\), \(g(4)=4^{2}-2=16-2 = 14\).

Answer:

The absolute maximum is \(23\) at \(x=-5\).