Explanation Given: The volume of water is V = π ( R h 2 − 1 3 h 3 ) , where h is the water level and R is the radius of sphere. Let the water level rises at a constant rate of 1. The graph is: Calculation: The volume of water is V = π ( R h 2 − 1 3 h 3 ) . Rate of water level increasing d h d t = 1 . Also, h = t . Part a: Find the derivative of V with respect to h . d V d t = π ( 2 R h − 1 3 ( 3 h 2 ) ) = π ( 2 R h − h 2 ) Find the second derivative of V with respect to h . d 2 V d t 2 = π ( 2 R − 2 h ) To find the inflection point substitute d 2 V d t 2 = 0 . π ( 2 R − 2 h ) = 0 2 R − 2 h = 0 2 R = 2 h R = h Thus, the inflection point occurs when the water level equal to the radius of the sphere

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.4, Problem 60E

To determine

a. Find the inflection point of V. Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.)

b. Plot V for R=1.

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Chapter 4.4, Problem 59E

Chapter 4.4, Problem 61E

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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a. Find the inflection point of V . Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.) b. Plot V for R = 1 .

Solution Summary: The author explains that the inflection point occurs when the water level equals the radius of the sphere.

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a. Find the inflection point of V. Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.)

b. Plot V for R=1.

Want to see the full answer?

Chapter 4 Solutions

a. Find the inflection point of V . Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.) b. Plot V for R = 1 .

Solution Summary: The author explains that the inflection point occurs when the water level equals the radius of the sphere.

Concept explainers

Videos

a. Find the inflection point of V. Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.) b. Plot V for R=1.

Want to see the full answer?

Chapter 4 Solutions

a. Find the inflection point of V. Also, tell that this agree with your conclusion in exercise 63. (Conclusion of exercise 63: When the sphere is half full then the inflection point occurs.)

b. Plot V for R=1.