To determine the correct response, we need to analyze the graph. Since I can't see the graph you are referring to, I'll summarize what each of the potential answers suggests about the extrema in the graph.
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There is one relative maximum and one relative minimum.
- This option suggests that the graph has one peak (relative maximum) and one trough (relative minimum) but no global maximum or minimum.
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There is one relative maximum, one relative minimum, and one absolute minimum.
- This indicates the graph has a peak, a trough, and a global low point (absolute minimum).
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There is one absolute maximum and one relative minimum.
- This means there is a global high point (absolute maximum) and a local low point (relative minimum).
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There is one relative maximum and one absolute minimum.
- This implies there is a local peak (relative maximum) and the lowest point on the graph (absolute minimum).
You should analyze the graph to see which conditions are met based on the definitions of relative and absolute extrema:
- Relative Maximum: A point where the function value is greater than all nearby function values.
- Relative Minimum: A point where the function value is less than all nearby function values.
- Absolute Maximum: The highest point over the entire domain of the function.
- Absolute Minimum: The lowest point over the entire domain of the function.
Once you examine the graph, select the statement that accurately describes the types of extrema present.
2 answers