Question

the function f is given by the graph below. 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.

Explanation:

Step1: Recall the definition of local extrema

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

Step2: Analyze the graph

Looking at the graph, we can see that at \(x = 2\), the function changes from decreasing to increasing. So, there is a local minimum at \(x = 2\). Also, at \(x=6\), the function changes from increasing to decreasing. So, there is a local maximum at \(x = 6\).

Answer:

Local minimum at \(x = 2\), local maximum at \(x = 6\)