Explanation Given: The length of the fence is 350 feet. Concept Used: Power rule of derivatives, d d x ( x n ) = n x n − 1 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Derivative of sum of functions: d d x ( f ( x ) + g ( x ) ) = d d x ( f ( x ) ) + d d x ( g ( x ) ) Constant product with derivative: d d x ( c f ( x ) ) = c d d x ( f ( x ) ) , where c is a Area of rectangle = Length × Width Perimeter of rectangle = 2 ( Length + Width ) Calculation: Let the length of the rectangular ostrich pen be x feet and width be y feet as shown in following figure: Since the total fencing material is 350 feet, so it must be equal to the perimeter of the rectangular pen. That is Perimeter of rectangle = 2 ( Length + Width ) 350 = 2 ( x + y ) ⇒ x + y = 350 2 ⇒ x + y = 175 ⇒ y = 175 − x ...... ( i ) And, the area of the rectangular ostrich pen is given by Area of rectangle = Length × Width A = x y A = x ( 175 − x ) ( using equation ( i ) ) A = 175 x − x 2 ...... ( i i ) Now, in order to maximize the area, find the critical points by setting the first derivative equal to zero

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ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.4, Problem 35A

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The dimension of the rectangular ostrich pen that enclose maximum possible area.

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Chapter 3.4, Problem 34S

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Chapter 3 Solutions

Calculus

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The dimension of the rectangular ostrich pen that enclose maximum possible area.

Solution Summary: The author calculates the perimeter of a rectangular ostrich pen, based on the length and width of the fence.

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The dimension of the rectangular ostrich pen that enclose maximum possible area.

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Chapter 3 Solutions