Question

question
identify the local maximum and local minimum of the function shown in the graph below.
provide your answer below:
the local maximum is at ( ) and the local minimum is at ( )

Explanation:

Step1: Understand local maximum and minimum

A local maximum is a point where the function changes from increasing to decreasing. A local minimum is a point where the function changes from decreasing to increasing.

Step2: Locate points on the graph

Looking at the graph, the function has a peak (local maximum) at \(x = 2\) with \(y=7\). The function has a valley (local minimum) at \(x=-1\) with \(y = 3\).

Answer:

The local maximum is at \((2,7)\) and the local minimum is at \((-1,3)\)