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 values at which g has a local maximum:
all local maximum values of g:

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = g(x)\) occurs at a point \(x = a\) if \(g(a)\geq g(x)\) for all \(x\) in some open interval containing \(a\). Visually, it is a "peak" on the graph.
Looking at the graph of \(y = g(x)\), the \(x -\)coordinates of the peak points are \(x=-4\) and \(x = 4\).

Step2: Find the local maximum values

The local maximum value is the \(y -\)coordinate of the local maximum point.
When \(x=-4\), \(y = 1\); when \(x = 4\), \(y=1\)

Answer:

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