Question

Check the boxes of the points where the graph has a local maximum A. 0 B. 1 C. 2 D. 3 E. 4 F. 5 G. 6 H. 7 Check the boxes of the points where the graph has a local minimum A. 0 B. 1 C. 2 D. 3 E. 4 F.

Answer 1

A. ☑ 0; B. ☑ 1; C. ☑ 2; D. ☑ 3; E. ☐ 4; F. ☐ 5; G. ☑ 6; H. ☑ 7

Step-by-step explanation:

In analyzing the graph for local maxima and minima, one needs to look for points where the slope of the graph changes from positive to negative for a local maximum and from negative to positive for a local minimum.

1. A local maximum occurs where the graph changes from increasing to decreasing. Looking at the graph, this happens at points 2, 6, and 7. So, boxes C, G, and H are checked.

2.A local minimum occurs where the graph changes from decreasing to increasing. In this case, points 1 and 3 exhibit this behavior. Therefore, boxes B and D are checked.

Points 4 and 5 do not represent local maxima or minima based on the characteristics mentioned. Understanding the behavior of the graph in terms of its slope is crucial for correctly identifying these points. The checked boxes reflect the positions of local maxima and minima on the graph.

Answer 2

The graph has a local maximum at points 2 and 6, and a local minimum at points 1 and 5.

Step-by-step explanation:

To determine the points where the graph has a local maximum and a local minimum, we need to analyze the behavior of the graph around each point. A local maximum occurs when the graph changes from increasing to decreasing, while a local minimum occurs when the graph changes from decreasing to increasing.

To check each point given, observe the behavior of the graph in the vicinity of that point. If the graph is increasing before that point and decreasing after, it is a local maximum. If the graph is decreasing before that point and increasing after, it is a local minimum. Based on this analysis, the graph has a local maximum at points C. 2 and G. 6, and a local minimum at points B. 1 and F. 5.