mark the local extrema on the following graph.

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, the function is increasing before (x = - 4) and decreasing after (x=-4), so there is a local maximum at (x = - 4). The (y) - value at (x=-4) is approximately (36). The function is decreasing before (x = 4) and increasing after (x = 4), so there is a local minimum at (x = 4). The (y) - value at (x = 4) is approximately (-45).

Answer:

Mark a dot at ((-4,36)) for the local maximum and a dot at ((4,-45)) for the local minimum.