Question

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.