Explanation Given information: The function is f ( x ) = ( x x 2 + 3 x + 12 ) 3 / 2 and the value of x is 1 . Formula used: The percent rate of change of f ( x ) at x is 100 f ′ ( x ) f ( x ) % Where, f ( x ) is the function. f ′ ( x ) is the first derivative of the function. Calculation: The function is f ( x ) = ( x x 2 + 3 x + 12 ) 3 / 2 . Apply chain rule and find the first derivative of f ( x ) as given below, f ′ ( x ) = d d x [ ( x x 2 + 3 x + 12 ) 3 / 2 ] = 3 2 [ ( x x 2 + 3 x + 12 ) 1 / 2 ⋅ d d x ( x x 2 + 3 x + 12 ) ] ( ∵ d d x ( x ) n = n ( x ) n − 1 ) = 3 2 [ ( x x 2 + 3 x + 12 ) 1 / 2 ( ( x 2 + 3 x + 12 ) ⋅ 1 − x ( 2 x + 3 ) ( x 2 + 3 x + 12 ) 2 ) ] ( ∵ d d x ( u v ) = v ⋅ d d x ( u ) − u ⋅ d d x ( v ) v 2 ) Further the simplification of the above derivative is, f ′ ( x ) = 3 2 [ ( x x 2 + 3 x + 12 ) 1 / 2 ( x 2 + 3 x + 12 − 2 x 2 − 3 x ( x 2 + 3 x + 12 ) 2 ) ] = 3 2 [ ( x x 2 + 3 x + 12 ) 1 / 2 ( 12 − x 2 ( x 2 + 3 x + 12 ) 2 ) ] = 3 2 [ ( 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 3.4, Problem 26E

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The percent rate of change of given function at x=1 .

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Chapter 3.4, Problem 25E

Chapter 3.4, Problem 27E

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Chapter 3 Solutions

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

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - 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Chapter 3 Solutions