step 1 of 2 : use the graph to determine the locations and type of the local extrema. write dne for all…

step 1 of 2 : use the graph to determine the locations and type of the local extrema. write dne for all extrema that do not exist. separate multiple answers with a comma, if necessary.

step 1 of 2 : use the graph to determine the locations and type of the local extrema. write dne for all extrema that do not exist. separate multiple answers with a comma, if necessary.

Answer

Explanation:

Step1: Recall local - extrema definition

Local maxima are points where the function changes from increasing to decreasing, and local minima are points where the function changes from decreasing to increasing.

Step2: Analyze the graph

Looking at the graph, we can see that the function changes from increasing to decreasing at a point near (x=- 2). This is a local maximum. Also, the function changes from decreasing to increasing at the origin ((0,0)), which is a local minimum.

Answer:

Local maximum at (x\approx - 2), local minimum at (x = 0)