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: 9781319323394

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 W/SAPLING ACCESS >IC<

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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

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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.