Answer:
- relative maximum of 4
- at x = 0
- relative minimum of 1
- at x = 3
- increasing on the intervals (-∞, 0) and (3, ∞)
- decreasing on the interval (0, 3)
- domain: all real numbers, (-∞, ∞)
- range: all real numbers, (-∞, ∞)
Step-by-step explanation:
You have successfully identified the relative maximum. The same procedure applies to identifying the relative minimum: look for a place where the curve goes up to the left and up to the right. The point (3, 1) is marked as that minimum, so is 1 at x=3.
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The curve is increasing everywhere except at the relative extrema and in the region between the maximum and minimum. It is decreasing between the maximum and minimum. (It has to go downhill to get from the maximum to the minimum.)
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The graph extends to infinity in all directions and is not undefined anywhere. As with all odd-degree polynomials, the domain and range are both "all real numbers."
