Question

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

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = g(x)\) is a point where the function changes from increasing to decreasing. The \(y -\)value of this point is the local maximum value, and the \(x -\)value is the value at which the local maximum occurs.

Step2: Identify local maximum values from the graph

Looking at the graph, the \(y -\)coordinates of the local maximum points are \(y = 1\) (there are two local maximum points with the same \(y -\)value).

Step3: Identify the \(x -\)values for local maxima

The \(x -\)coordinates of the local maximum points are \(x=-4\) and \(x = 4\) (these are the values of \(x\) where the function \(g(x)\) has a local maximum).

Answer:

All local maximum values of \(g\): \(1\)
All values at which \(g\) has a local maximum: \(-4,4\)