Explanation Given information: The function is f ( x ) = x + 1 x 3 + x + 1 and the value of x is 2 . 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 first derivative of f ( x ) is calculated as, f ′ ( x ) = d d x [ x + 1 x 3 + x + 1 ] = ( x 3 + x + 1 ) d d x ( x + 1 ) − ( x + 1 ) d d x ( x 3 + x + 1 ) ( x 3 + x + 1 ) 2 ( ∵ d d x ( u v ) = v ⋅ d d x ( u ) − u ⋅ d d x ( v ) v 2 ) = ( x 3 + x + 1 ) ( 1 ) − ( x + 1 ) ( 3 x 2 + 1 ) ( x 3 + x + 1 ) 2 ( ∵ d d x ( x ) n = n ( x ) n − 1 ) = ( x 3 + x + 1 ) − ( 3 x 3 + x + 3 x 2 + 1 ) ( x 3 + x + 1 ) 2 Further the simplification of the above equation is, f ′ ( x ) = x 3 + x + 1 − 3 x 3 − x − 3 x 2 − 1 ( x 3 + x + 1 ) 2 = − 2 x 3 − 3 x 2 ( x 3 + x + 1 ) 2 The percent rate of change of f ( x ) at x is calculated as, 100 f ′ ( x ) f ( x )

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 3.4, Problem 25E

To determine

The percent rate of change of f(x) at x=2 .

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Chapter 3.4, Problem 24E

Chapter 3.4, Problem 26E

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Chapter 3 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The percent rate of change of f ( x ) at x = 2 .

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The percent rate of change of f(x) at x=2 .

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Chapter 3 Solutions