Question

locating local maximum and minimum function values
use the graph to find the local minimum and the local maximum for the given function. hover over (or tap) a point to see its coordinates.
over the interval -1, -1, the local minimum is
over the interval -1, 0, the local maximum is
over the interval 0, 2, the local minimum is

Explanation:

Step1: Analyze interval [-1, 1]

By observing the graph, in the interval [-1, 1], the lowest - point within this interval is at the bottom of the curve. The y - value at this point is - 20.

Step2: Analyze interval [-1, 0]

In the interval [-1, 0], the highest - point within this interval is at the point where the curve changes its direction. The y - value at this point is 5.

Step3: Analyze interval [0, 2]

In the interval [0, 2], the lowest - point within this interval is at the bottom of the curve. The y - value at this point is - 30.

Answer:

Over the interval [-1, 1], the local minimum is - 20.
Over the interval [-1, 0], the local maximum is 5.
Over the interval [0, 2], the local minimum is - 30.