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 maxima

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 \(x = 1\), the function changes from increasing (as we approach \(x = 1\) from the left) to decreasing (as we move to the right of \(x = 1\)).

Answer:

Local maximum at \(x = 1\)