Question

here is a graph of the function f. use the graph to find the following. if there is more than one answer, separate them with commas. all local maximum values of f: all values at which f has a local maximum:

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function \(y = f(x)\) is a point where the function value is greater than or equal to the values of the function in a small interval around that point. Visually, it is a "peak" on the graph.

Step2: Identify local - maximum points on the graph

Looking at the graph, we can see that the function has local maxima at two points. The \(y\) - values of these local maxima are the local maximum values of \(f\), and the \(x\) - values are the values at which \(f\) has a local maximum.
The first local maximum occurs at \(x=- 2\) with \(y = 3\), and the second local maximum occurs at \(x = 3\) with \(y=1\).

Answer:

All local maximum values of \(f\): \(3,1\)
All values at which \(f\) has a local maximum: \(-2,3\)