Question

what is a local maximum of the function graphed below?

Explanation:

Step1: Recall local - maximum definition

A local maximum is a point on the graph where the function value is greater than the values at nearby points.

Step2: Analyze the graph

By observing the graph, we can see that around \(x = - 5\), the function value is higher than the values of the function immediately to the left and right of \(x=-5\). The \(y\) - value at this local - maximum point is approximately \(y = - 1\).

Answer:

The local maximum occurs at the point \((-5,-1)\)