During a flood, the water level in a river first rose faster and faster, then rose more

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During a flood, the water level in a river first rose faster and faster, then rose more and more slowly until it reached its highest point, then went back down to its pre-flood level. Consider water depth as a function of time.
(a) Is the time of highest water level a critical point or an inflection point of this function?
(b) Is the time when the water first began to rise more slowly a critical point or an inflection point?

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Applied Calculus

ISBN: 9781119275565

6th Edition

Authors: Deborah Hughes Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, Sheldon P. Gordon, David O. Lomen, David Lovelock, William G. McCallum, Brad G. Osgood, Andrew Pasquale

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