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Height vs. volume The figure shows six containers, each of
Chapter 7, Problem 65E(choose chapter or problem)
Height vs. volume The figure shows six containers, each of which is filled from the top. Assume that water is poured into the containers at a constant rate and each container is filled in 10 s. Assume also that the horizontal cross sections of the containers are always circles. Let h(t) be the depth of water in the container at time t for \(0 \leq t \leq 10\).
a. For each container, sketch a graph of the function y = h(t) for \(0 \leq t \leq 10\).
b. Explain why h is an increasing function.
c. Describe the concavity of the function. Identify inflection points when they occur.
d. For each container, where does h' (the derivative of h) have an absolute maximum on [0, 10]?
Questions & Answers
QUESTION:
Height vs. volume The figure shows six containers, each of which is filled from the top. Assume that water is poured into the containers at a constant rate and each container is filled in 10 s. Assume also that the horizontal cross sections of the containers are always circles. Let h(t) be the depth of water in the container at time t for \(0 \leq t \leq 10\).
a. For each container, sketch a graph of the function y = h(t) for \(0 \leq t \leq 10\).
b. Explain why h is an increasing function.
c. Describe the concavity of the function. Identify inflection points when they occur.
d. For each container, where does h' (the derivative of h) have an absolute maximum on [0, 10]?
ANSWER:
Solution: Step1 a. For each container, a graph of the function y = )for 0 t 10 Step2 (b) h is an increasing fun