Question

identify local extrema and intervals on which the function is decreasing and increasing. choose the best description for the plotted point (-6, -1) on the curve. a. a local minimum b. a local maximum c. neither a minimum nor a maximum -10, 10 by -50, 50

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 (-6, - 1)

Looking at the graph around the point (-6, - 1), if we consider a small interval around x = - 6, there are points with lower function values and points with higher function values. So, it is neither a local minimum nor a local maximum.

Answer:

C. neither a minimum nor a maximum