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? The time of highest water level is a critical point of this function. (b) Is the time when the water first began to rise more slowly a critical point or an inflection point? The time when the water first began to rise more slowly is an inflection point v

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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I cannot visualize this question. Could you please draw a graph and label all the critical points and inflections?

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?
The time of highest water level is
a critical point
of this function.
(b) Is the time when the water first began to rise more slowly a critical point or an inflection point?
The time when the water first began to rise more slowly is
an inflection point v
Transcribed Image Text: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? The time of highest water level is a critical point of this function. (b) Is the time when the water first began to rise more slowly a critical point or an inflection point? The time when the water first began to rise more slowly is an inflection point v
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