Question

here is a graph of the function \\(h\\).

use the graph to find the following.
if there is more than one answer, separate them with commas.

all local maximum values of \\(h\\):
all values at which \\(h\\) has a local maximum:

Explanation:

Identify local maximum points on the graph

A local maximum occurs at a point where the function changes from increasing to decreasing, forming a "peak" on the graph. Looking at the graph of \(h\), there are two distinct peaks:

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

Determine the local maximum values

The local maximum values of a function are the \(y\)-values (outputs) at these peak points.

• From the point \((-3, 3)\), the local maximum value is \(3\).
• From the point \((2, 4)\), the local maximum value is \(4\).

Thus, the local maximum values of \(h\) are \(3, 4\).

Determine the values at which the function has a local maximum

The values at which \(h\) has a local maximum refer to the \(x\)-values (inputs) where these peaks occur.

• The peak at \((-3, 3)\) occurs at \(x = -3\).
• The peak at \((2, 4)\) occurs at \(x = 2\).

Thus, the values at which \(h\) has a local maximum are \(-3, 2\).

Answer:

Question 1

All local maximum values of \(h\): <blank>3, 4</blank>

Question 2

All values at which \(h\) has a local maximum: <blank>-3, 2</blank>