(a) Explanation Given: The function is f ( x ) = x ( x 2 − 1 ) 2 x − 2 . Calculation: Differentiate the given function f with respect to x , f ′ ( x ) = ( x − 2 ) d d x ( x ( x 2 − 1 ) 2 ) − x ( x 2 − 1 ) 2 d d x ( x − 2 ) ( x − 2 ) 2 = ( x − 2 ) [ ( x 2 − 1 ) 2 d d x ( x ) + x d d x ( ( x 2 − 1 ) 2 ) ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = ( x − 2 ) [ 1 2 x ( x 2 − 1 ) 2 + 4 x ( x 2 − 1 ) x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = ( x − 2 ) [ ( x 2 − 1 ) 2 2 x + 4 x 7 2 − 4 x x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 Further solve the above equation. f ′ ( x ) = ( x − 2 ) [ ( x 2 − 1 ) 2 + 4 ⋅ 2 x 7 2 x − 4 ⋅ 2 x x x 2 x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = ( x − 2 ) [ ( x 2 − 1 ) 2 + 8 x 4 − 8 x 2 2 x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = ( x − 2 ) [ x 4 − 2 x 2 + 1 + 8 x 4 − 8 x 2 2 x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = ( x − 2 ) [ 9 x 4 − 10 x 2 + 1 2 x ] − x ( x 2 − 1 ) 2 ( x − 2 ) 2 Further, solve the above equation. f ′ ( x ) = ( 9 x 4 − 10 x 2 + 1 ) ( x − 2 ) 2 x − x ( x 2 − 1 ) 2 ( x − 2 ) 2 = 7 x 5 − 18 x 4 − 6 x 3 + 20 x 2 − x − 2 2 x ( x − 2 ) 2 = 7 x 5 − 18 x 4 − 6 x 3 + 20 x 2 − x − 2 2 x ( x − 2 ) 2 The given first function is, f ( x ) = x ( x 2 − 1 ) 2 x − 2 The second function is, f ′ ( x ) = 7 x 5 − 18 x 4 − 6 x 3 + 20 x 2 − x − 2 2 x ( x − 2 ) 2 To plot the graph of given functions follow the steps below (b) To determine The relative extrema of f .

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 4.1, Problem 8TE

(a)

To determine

To find: The increasing and decreasing interval of given function f by ZOOM and TRACE feature of graphing calculator.

(b)

To determine

The relative extrema of f.

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Chapter 4.1, Problem 7TE

Chapter 4.1, Problem 9TE

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Chapter 4 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E

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The increasing and decreasing interval of given function f by ZOOM and TRACE feature of graphing calculator.

Solution Summary: The author explains the increasing and decreasing intervals of given function f by ZOOM and TRACE feature of graphing calculator.