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
local minimum at:
local maximum at:

Explanation:

Step1: Recall the definition of local minimum

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

Step2: Recall the definition of local maximum

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

Step3: Analyze the graph

Looking at the graph, we can see that the function has a local minimum at \(x = - 1\) (since the function changes from decreasing to increasing at that point) and a local maximum at \(x=-3\) (since the function changes from increasing to decreasing at that point).

Answer:

Local minimum at: \(x = - 1\)
Local maximum at: \(x=-3\)