Question

which interval for the graphed function contains the local maximum?
-3,-2
-2,0
0,2
2,4

Explanation:

Step1: Recall local maximum definition

A local maximum is a point where the function changes from increasing to decreasing, and its \( x \)-coordinate lies within an interval.

Step2: Identify local max \( x \)-coordinate

The local maximum point is \( (1.55, 10.8) \), so its \( x \)-value is \( 1.55 \).

Step3: Check which interval contains \( 1.55 \)

• For \( [-3, -2] \): \( 1.55

otin [-3, -2] \).

• For \( [-2, 0] \): \( 1.55

otin [-2, 0] \).

• For \( [0, 2] \): \( 0 \leq 1.55 \leq 2 \), so \( 1.55 \in [0, 2] \).
• For \( [2, 4] \): \( 1.55

otin [2, 4] \).

Answer:

C. \([0, 2]\)