Question

the function f is given by the graph below. step 2 of 2: determine the value(s) of the local extrema you identified in the previous step. write dne for all extrema that do not exist. separate multiple answers with a comma. if necessary.

Explanation:

Step1: Recall the definition of local extrema

A local maximum is a point where the function changes from increasing to decreasing. A local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze the graph

Looking at the graph, we can see that there is a local minimum at \(x = - 6\) (where \(y = 0\)) and a local maximum. To find the \(y\) - value of the local maximum, we observe the \(y\) - coordinate of the peak. The local maximum occurs at \(y = 2\).

Answer:

\(0,2\)