Question

here is a graph of the function f. use the graph to find the following. if there is more than one answer, separate them with commas. all values at which f has a local maximum: all local maximum values of f:

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function occurs at a point where the function changes from increasing to decreasing.

Step2: Identify x - values

Looking at the graph, the function changes from increasing to decreasing at \(x = 1\). So the value of \(x\) at which \(f\) has a local maximum is \(x = 1\).

Step3: Find local - maximum value

To find the local - maximum value, we look at the \(y\) - coordinate of the point with \(x = 1\). From the graph, when \(x = 1\), \(y=1\).

Answer:

All values at which \(f\) has a local maximum: \(1\)
All local maximum values of \(f\): \(1\)