which interval contains a local minimum for the graphed function?\n-4,-2.5\n-2,-1\n1,2\n2.5,4

Answer:

D. $[2.5,4]$

Explanation:

Step1: Understand local minimum

A local minimum is a point where the function value is less than or equal to the values of the function in a small - neighborhood around it.

Step2: Analyze intervals

• For $[-4,-2.5]$: The function is decreasing in this interval, no local minimum.
• For $[-2,-1]$: The function is increasing in this interval, no local minimum.
• For $[1,2]$: The function is increasing in this interval, no local minimum.
• For $[2.5,4]$: The function has a local minimum near $x = 3$ within this interval as the function changes from decreasing to increasing around $x = 3$.