Use the graphing tool to find the local minimum and the local maximum for the given function.

over the interval [-3, -1], the local minimum is

a) -3
b) -2
c) -1
d) 0

over the interval [-1, 0], the local maximum is

a) -1
b) 0
c) 1.5
d) 4.39

over the interval [0, 3], the local minimum is

a) -40
b) -32
c) -18
d) 0

Over the interval [-3, 1], the local minimum is 0, since . Right choice: D. Over the interval [-1, 0], the local maximum is 4.39, since . Right choice: D.Over the interval [0, 3], the local minimum is -32, since . Right choice: B.

Given a function that is continuous for an interval , , then there is a local minimum and local maximum if and only if:

Local minimum:

, (1)

Local maximum:

(2)

Based on these facts, we proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0, since . Right choice: D.Over the interval [-1, 0], the local maximum is 4.39, since . Right choice: D. Over the interval [0, 3], the local minimum is -32, since . Right choice: B.

We kindly invite to check this question on maxima and minima: link