To determine the relative maximum of the polynomial function \( h(x) \) based on the description of the S-shaped curve, you would typically look for points where the curve changes direction from increasing to decreasing.
- A relative maximum occurs where the graph reaches a peakâgoing up to a certain point and then descending.
- If the curve is S-shaped, it likely has at least one peak and one trough.
Given the provided answer choices, the options indicate the possibility of relative maxima at \( x = 0 \) or \( x = 2 \) and state that there may be no relative maximum at all.
Without the image, I cannot definitively identify which option is correct, but based on a standard S-shaped curve, you would generally expect to find a relative maximum where the slope of the curve changes from positive to negative.
If there's an evident peak at \( x = 0 \) in the S-curve and no peak at \( x = 2 \) that is higher than the neighboring points, the correct response would be:
- There is a relative maximum at \( x = 0 \).
Conversely, if the highest point is at \( x = 2 \) and it is higher than at \( x = 0 \), then the correct response would be:
- There is a relative maximum at \( x = 2 \).
If the S-curve does not have any clear peaks, then you would choose:
- There is no relative maximum in this graph.
If there is also a mention of a relative minimum at \( x=1 \), that would be a critical point to note as well but does not directly answer the question about relative maximums.
You would need to visually check the graph to make the final determination.
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