question identify the local maximum and local minimum of the function shown in the graph below. provide your…

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 ( )

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 ( )

Answer

Explanation:

Step1: Recall local - max/min definition

A local maximum is a point where the function value is greater than the values at nearby points, and a local minimum is a point where the function value is less than the values at nearby points.

Step2: Identify local maximum from the graph

Looking at the graph, the function reaches a peak at the point $(3,4)$. The $y$ - value of 4 at $x = 3$ is greater than the $y$ - values of the points immediately around it.

Step3: Identify local minimum from the graph

The function reaches a trough at the point $(5,1)$. The $y$ - value of 1 at $x = 5$ is less than the $y$ - values of the points immediately around it.

Answer:

The local maximum is at $(3,4)$ and the local minimum is at $(5,1)$