a. Explanation Given: The width w of the rectangle is decreasing at the rate 3 inches per second and the height h is increasing at the rate 3 inches per second. The initial width and height of the rectangle are 100 inches and 75 inches respectively. Formulaused: The area of a rectangle of width w and height h is given by A = w × h . Since, w and h are function of time so the area A . Calculation: The area of the rectangle is A ( t ) = w ( t ) × h ( t ) ............ (1) Differentiating result (1) with respect to‘ t’ d A d t = w × d h d t + d w d t × h ............ (2) The width of rectangle decreasing at the rate 3 inches per seconds, i.e., d w d t =- 3 inches per second and the height is increasing at the rate 3 inches per second, i b. To determine The interval of width and the height of the rectangle and on what time interval the problem makes the sense. c. To determine To find: In terms of width ( w ) and height ( h ) of the rectangle when the area is increasing and when decreasing.

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.5, Problem 58A

To determine

To find:The rate of change of area of rectangle in terms of its width and height.

To determine

The interval of width and the height of the rectangle and on what time interval the problem makes the sense.

To determine

To find: In terms of width ( w ) and height ( h ) of the rectangle when the area is increasing and when decreasing.

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Chapter 3.5, Problem 57A

Chapter 3.5, Problem 59A

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Chapter 3 Solutions

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The rate of change of area of rectangle in terms of its width and height.

Solution Summary: The author calculates the rate of change of area of a rectangle in terms of its width and height.

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To find:The rate of change of area of rectangle in terms of its width and height.

The interval of width and the height of the rectangle and on what time interval the problem makes the sense.

To find: In terms of width ( w ) and height ( h ) of the rectangle when the area is increasing and when decreasing.

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Chapter 3 Solutions