Question

find the locations and values of all relative extrema for the function with the graph below. the function has a relative maximum of 3 at x = the function has a relative minimum of -5 at x =

Explanation:

Step1: Identify relative maximum

A relative maximum is a point where the function changes from increasing to decreasing. Looking at the graph, at \(x = 1\), the function has a relative maximum value of \(y = 1\) (since the \(y -\) coordinate at the peak is \(1\)).

Step2: Identify relative minimum

A relative minimum is a point where the function changes from decreasing to increasing. Looking at the graph, at \(x=- 1\), the function has a relative minimum value of \(y=-3\) (since the \(y -\) coordinate at the trough is \(-3\)).

Answer:

The function has a relative maximum of \(1\) at \(x = 1\) and a relative minimum of \(-3\) at \(x=-1\).