Question

identify local extrema and intervals on which the function is decreasing and increasing. choose the best description for the plotted point (-2, -1) on the curve. a. a local minimum b. a local maximum c. neither a minimum nor a maximum

Explanation:

Step1: Recall local - extrema definition

A local minimum is a point where the function value is less than or equal to the values at nearby points. A local maximum is a point where the function value is greater than or equal to the values at nearby points.

Step2: Analyze the point (-2,-1)

Looking at the graph (not provided in full details here but based on the concept), if the function has a "valley - like" shape at the point (-2,-1), it is a local minimum. If it has a "peak - like" shape, it is a local maximum. If the function is just passing through without any such change in the trend, it is neither. From the description, we assume we can see the trend around the point. If the function is increasing on one side and decreasing on the other side of the point (-2,-1), it is a local maximum. If it is decreasing on one side and increasing on the other side, it is a local minimum. If the function is either increasing or decreasing on both sides of the point, it is neither.

Answer:

We need to analyze the graph around the point (-2,-1). If the function is decreasing to the left and increasing to the right of (-2,-1), the answer is A. a local minimum. If the function is increasing to the left and decreasing to the right of (-2,-1), the answer is B. a local maximum. If the function is either increasing or decreasing on both sides of (-2,-1), the answer is C. neither a minimum nor a maximum. Without the full - view of the graph's behavior around the point, we can't give a definite single - choice answer. But the general method to determine is as described above.