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 definitions

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: Identify the points on the graph

Looking at the graph, for the local maximum: the \(x\) - coordinate is \(3\) and the \(y\) - coordinate is \(7\). For the local minimum: the \(x\) - coordinate is \(-1.5\) (approximate, since it's at \(x = - 1.5\) as per the grid) and the \(y\) - coordinate is \(0.8\) (approximate, since it's at \(y = 1\) as per the grid).

Answer:

The local maximum is at \((3,7)\) and the local minimum is at \((-1.5,1)\)