Explanation Given information: The perimeter of the rectangle is 64 cm. 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 be the length and y be the width of the rectangle. Then the perimeter of the rectangle is 2 ( x + y ) = 64 . x + y = 32 The area is given by A ( x ) = x y = x ( 32 − x ) = 32 x − x 2 Differentiating A ( x ) with respect to ‘x’, we get A ' ( x ) = 32 − 2 x Equating

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.3, Problem 38P

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Length of the sides of the rectangle giving the maximum area.

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Chapter 4.3, Problem 37P

Chapter 4.3, Problem 39P

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Length of the sides of the rectangle giving the maximum area.

Solution Summary: The author explains that the perimeter of the rectangle is 64 cm, and the area is given by cA(x)=xy.

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To find: Length of the sides of the rectangle giving the maximum area.

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Chapter 4 Solutions

To find:

Length of the sides of the rectangle giving the maximum area.