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.

answer

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, at \(x = - 7\), the function changes from decreasing to increasing (local minimum). At \(x=-2\), the function changes from increasing to decreasing (local maximum).

Answer:

Local minimum at \(x=-7\), local maximum at \(x = - 2\)