Explanation Given information: The cost of removing x % of the toxic pollutant in millions of dollars is, C ( x ) = 0.2 x 100 − x (1) Formula used : The quotient rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) [ g ( x ) ] 2 The above formula is defined when the denominator g ( x ) ≠ 0 . Calculation: Use the quotient rule of differentiation for the equation (1) to get the derivative function C ′ ( x ) . C ′ ( x ) = d d x [ 0.5 x 100 − x ] = ( 100 − x ) ⋅ d d x ( 0.5 x ) − ( 0.5 x ) ⋅ d d x ( 100 − x ) ( 100 − x ) 2 = ( 100 − x ) ⋅ ( 0.5 ) − ( 0.5 x ) ⋅ ( − 1 ) ( 100 − x ) 2 = 50 − 0.5 x + 0.5 x ( 100 − x ) 2 ( Apply distributive property ) Further solve the above equation for C ′ ( x )

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.2, Problem 53E

To determine

To find: The values of C′(80) , C′(90) , C′(95) , C′(99) and explain the result that gives the cost of removing all of the pollutant

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Chapter 3.2, Problem 52E

Chapter 3.2, Problem 54E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The values of C ′ ( 80 ) , C ′ ( 90 ) , C ′ ( 95 ) , C ′ ( 99 ) and explain the result that gives the cost of removing all of the pollutant

Solution Summary: The author explains the quotient rule of differentiation for the equation to get the derivative function.

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To find: The values of C′(80) , C′(90) , C′(95) , C′(99) and explain the result that gives the cost of removing all of the pollutant

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Chapter 3 Solutions