question\nidentify the local maximum and local minimum of the function shown in the graph below.\nprovide…

question\nidentify the local maximum and local minimum of the function shown in the graph below.\nprovide your answer below.\nthe local maximum is at ( ) and the local minimum is at ( )

question\nidentify the local maximum and local minimum of the function shown in the graph below.\nprovide your answer below.\nthe local maximum is at ( ) and the local minimum is at ( )

Answer

Explanation:

Step1: Recall local - max/min definition

Local maximum is a point where the function changes from increasing to decreasing, and local minimum is a point where the function changes from decreasing to increasing.

Step2: Identify local maximum on the graph

Looking at the graph, the function changes from increasing to decreasing at the point with (x=- 1) and (y = 4). So the local maximum occurs at the point ((-1,4)).

Step3: Identify local minimum on the graph

The function changes from decreasing to increasing at the point with (x = 1) and (y=-1). So the local minimum occurs at the point ((1,-1)).

Answer:

The local maximum is at ((-1,4)) and the local minimum is at ((1,-1))