Based on the description of the W-shaped curve, it would typically have multiple peaks and valleys.
In a W shape, you would generally find:
- One peak at the top of one of the W's arms, which would be the relative maximum.
- Valleys at the lowest points in the W's shape, which would be relative minima.
- Additionally, depending on the overall highest and lowest points of the curve in relation to the entire plotted range, there could be an absolute maximum and/or minimum.
From the options provided:
-
If the graph contains one highest point (which is a relative maximum) and one lowest point within the range (which is an absolute or relative minimum), the correct response might be "There is one relative maximum and one absolute minimum."
-
If the graph has both an absolute maximum (the highest point on the curve in relation to the entire graph) and a relative minimum (the lowest point where the curve dips), then the correct response would be “There is one absolute maximum and one relative minimum.”
-
If the graph has both a relative maximum and minimum but does not touch the highest and lowest points of the y-axis, then the correct response would be "There is one relative maximum and one relative minimum.”
Given that the question specifies various types of extrema, it is crucial to identify both relative and absolute points.
Without the exact visual, an appropriate answer could be "There is one relative maximum, one relative minimum, and one absolute minimum," if the described extrema warrant it.
Thus, if the W-shape supports multiple extrema types based on the question parameters, the most inclusive answer that covers potential minima and maxima might be:
"There is one relative maximum, one relative minimum, and one absolute minimum."