Let f(x) = 2x^{3}+9. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

1. f is increasing on the intervals:
2. f is decreasing on the intervals:
3. The relative maxima of f occur at x =
4. The relative minima of f occur at x =

1 answer

f' = 6x^2+9
clearly, f' is always positive, so there are no extrema, and no intervals where f is decreasing.

Just think of what you know of the curve y=x^3
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