Question

Question

Which of the following most accurately identifies the types of extrema in the graph?

(1 point)
Responses

There is one relative maximum, one relative minimum, and one absolute minimum.
There is one relative maximum, one relative minimum, and one absolute minimum.

There is one relative maximum and one relative minimum
There is one relative maximum and one relative minimum

​​There is one absolute maximum and one relative minimum.
​​ There is one absolute maximum and one relative minimum.

There is one relative maximum and one absolute minimum

Answer 1

To accurately identify the types of extrema in a graph, we need to consider the definitions:

• Relative maximum: A point higher than all nearby points.
• Relative minimum: A point lower than all nearby points.
• Absolute maximum: The highest point over the entire graph.
• Absolute minimum: The lowest point over the entire graph.

Given your options, please refer to the graph you have in mind. The correct response will depend on how many of each type of extremum is present within that specific graph.

If the graph has one point that is the highest overall and another point that is the lowest overall, then "There is one absolute maximum and one absolute minimum" would be correct.

If the graph has peaks and valleys with one of each, then "There is one relative maximum and one relative minimum" would be correct.

However, without seeing the graph, it's impossible to definitively choose the correct response. Please examine your graph carefully based on the definitions above to select the appropriate option.