Explanation Given information: The sum of three nonnegative numbers is 36. One of the numbers is twice one of the other numbers. Fact used: If f ' changes from negative to positive at p, then f has a local minimum at p. If f ' changes from positive to negative at p, then f has a local maximum at p. Calculation: Let x , 2 x , y be the three nonnegative numbers. The sum of three nonnegative numbers is 36. (Given) ⇒ x + 2 x + y = 36 ⇒ 3 x + y = 36 Their product is given by P ( x ) = x .2 x . y = 2 x 2 y = 2 x 2 ( 36 − 3 x ) = 72 x 2 − 6 x 3 Differentiating P ( x ) with respect to ‘x’, we get P ' ( x ) = 144 x − 18 x 2 Equating P ' ( x ) <

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 4.3, Problem 37P

To determine

To find:

The maximum value of the product of the three nonnegative numbers.

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Chapter 4.3, Problem 36P

Chapter 4.3, Problem 38P

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The maximum value of the product of the three nonnegative numbers.

Solution Summary: The author explains that the sum of three nonnegative numbers is 36. If f' changes from positive to negative at p, then it has a local minimum.

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To find: The maximum value of the product of the three nonnegative numbers.

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Chapter 4 Solutions

To find:

The maximum value of the product of the three nonnegative numbers.