Question

which interval for the graphed function contains the local maximum?
-1,0
1,2
2,3
3,4

Explanation:

Step1: Recall local maximum definition

A local maximum is a point where the function changes from increasing to decreasing (the graph has a "peak" in that interval).

Step2: Analyze each interval

• For \([-1, 0]\): The graph is decreasing (from a high value to a low at \(x = 0\)), no peak.
• For \([1, 2]\): The graph rises to a peak (changes from increasing to decreasing) in this interval.
• For \([2, 3]\): The graph is decreasing (from the peak to a trough), no peak.
• For \([3, 4]\): The graph is increasing (from the trough to a high), no peak.

Answer:

[1, 2]