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:

Identify local maximum points

We look for peaks on the graph of \(f\).
These are points where the function changes from increasing to decreasing.
From the graph, we observe two peaks marked with solid dots:

• One peak is at the point \((-2, 3)\).
• The other peak is at the point \((4, 2)\).

Find values at which f has a local maximum

The "values at which \(f\) has a local maximum" refer to the \(x\)-coordinates of these peak points.
The \(x\)-coordinates of our identified peaks are:

• \(x = -2\)
• \(x = 4\)

Thus, the values at which \(f\) has a local maximum are \(-2, 4\).

Find all local maximum values of f

The "local maximum values of \(f\)" refer to the \(y\)-coordinates (the function values) at those peaks.
The \(y\)-coordinates of our identified peaks are:

• \(y = 3\)
• \(y = 2\)

Thus, the local maximum values of \(f\) are \(3, 2\) (or \(2, 3\)).

Answer:

All values at which \(f\) has a local maximum: <blank>-2, 4</blank>

All local maximum values of \(f\): <blank>3, 2</blank>