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=
(type an integer. use a comma to separate answers as needed.) b. there are no local maxima.

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = f(x)\) occurs at a point \(x = a\) if \(f(a)\geq f(x)\) for all \(x\) in some open interval containing \(a\).

Step2: Analyze the graph

Looking at the graph of the function \(y = f(x)\), we can see that the function has two local maximum points. By observing the \(x -\)coordinates of these points (assuming the grid - based on integer values), we find that the \(x -\)values at which the local maxima occur are \(x=-2,x = 1\)

Answer:

A. \(x=-2,1\)