Question

here is a graph of the function g.
your answer
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: 2

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 \(a\). Graphically, it is a point where the function changes from increasing to decreasing.

Step2: Identify \(x -\)values of local maxima

Looking at the graph of \(y = g(x)\), we observe the points where the function has a "peak". The \(x -\)coordinates of these peaks are \(x=-1,x = 2\)

Answer:

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