Question

use the graph of the function f given below to answer the questions. list the values of x at which f has a local maximum. select the correct choice below and fill in any answer boxes within your choice. a. x = - 3, 1 (type an integer. use a comma to separate answers as needed.) b. there are no local maxima. what are these local maxima, if they exist? select the correct choice below and fill in any answer boxes within your choice. a. the local maxima are. (type an integer. use a comma to separate answers as needed.) b. there are no local maxima.

Explanation:

Step1: Recall local - maximum definition

A local maximum occurs at a point where the function changes from increasing to decreasing.

Step2: Identify local - maximum points on the graph

By observing the graph, the function changes from increasing to decreasing at \(x=-3\) and \(x = 1\).

Step3: Determine the local - maximum values

The \(y\) - values at \(x=-3\) and \(x = 1\) are the local maxima. From the graph, the local maximum value at \(x=-3\) and \(x = 1\) is \(y = 3\) (by estimating the height of the peaks on the graph).

Answer:

A. \(x=-3,1\)
A. The local maxima are \(3\)