Question

use the graph to find:
(a) the numbers, if any, at which f has a local maximum. what are these local maxima?
(b) the numbers, if any, at which f has a local minimum. what are these local minima?
select the correct choice below and fill in any answer boxes within your choice.
a. the local maxima is/are y = 3
(type an integer. use a comma to separate answers as needed.)
b. there are no local maxima.
(b) select the correct choice below and fill in any answer boxes within your choice.
a. the value(s) of x at which f has a local minimum is/are x = -2,1
(type an integer. use a comma to separate answers as needed.)
b. there are no values of x at which f has a local minimum.
select the correct choice below and fill in any answer boxes within your choice.
a. the local minima is/are y =
(type an integer. use a comma to separate answers as needed.)
b. there are no local minima.

Explanation:

Step1: Analyze local minima

Local minima occur at the lowest points in a neighborhood. Looking at the graph, the function has local minima at \(x = - 2\) and \(x = 1\). The \(y\) - values at these points are found by substituting the \(x\) - values into the function (or reading from the graph). When \(x=-2\), \(y = 0\) and when \(x = 1\), \(y=0\).

Answer:

A. The local minima is/are \(y = 0\)