Question

which interval for the graphed function has a local minimum of 0?
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Explanation:

Step1: Understand the concept of local minimum

A local minimum of a function is a point where the function has a lower value compared to its neighboring points.

Step2: Analyze the intervals

• For the interval \([-3, - 2]\): Looking at the graph, we can see that the function is decreasing in this interval.
• For the interval \([-2,0]\): The function is increasing in this interval.
• For the interval \([0,2]\): The function is decreasing in this interval.
• For the interval \([2,4]\): The function is increasing in this interval.

The local minimum occurs at the point where the function changes from decreasing to increasing. From the analysis of the intervals, we can see that at \(x = 2\) (the end - point of the interval \([0,2]\) and start - point of \([2,4]\)), the function has a local minimum.

Answer:

\([2,4]\)