Which of the following most accurately identifies the types of extrema in the graph?
(1 point)
Responses
There is one absolute maximum and one relative minimum.
There is one absolute maximum and one relative minimum.
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 absolute minimum.
There is one relative maximum and one absolute minimum.
There is one relative maximum and one relative minimum.
There is one relative maximum and one relative minimum.
To accurately identify the types of extrema in a graph, we need to understand the definitions of each term.
1. Relative maximum: This is the highest point in a particular section of a graph, compared to the points immediately before and after it.
2. Relative minimum: This is the lowest point in a particular section of a graph, compared to the points immediately before and after it.
3. Absolute maximum: This is the highest point on the entire graph, considering all sections and points.
4. Absolute minimum: This is the lowest point on the entire graph, considering all sections and points.
Based on the given options, the most accurate identification of the types of extrema in the graph is:
"There is one relative maximum and one relative minimum."
To determine the types of extrema in the graph, we need to understand the definitions of absolute maximum, relative maximum, absolute minimum, and relative minimum.
- Absolute maximum: The highest point on the entire graph.
- Relative maximum: The highest point within a specific interval.
- Absolute minimum: The lowest point on the entire graph.
- Relative minimum: The lowest point within a specific interval.
Now, to identify the types of extrema in the graph, we need to analyze the given options:
- Option 1: "There is one absolute maximum and one relative minimum."
- Option 2: "There is one relative maximum, one relative minimum, and one absolute minimum."
- Option 3: "There is one relative maximum and one absolute minimum."
- Option 4: "There is one relative maximum and one relative minimum."
Based on these options, the most accurate identification of the extrema in the graph is Option 4: "There is one relative maximum and one relative minimum." This means that there is a point on the graph that is the highest within a certain interval (relative maximum), as well as a point that is the lowest within that same interval (relative minimum).