Explanation The proof is given by a counterexample. The functions are given by f ( x ) = cos x and g ( x ) = sin x . Find the derivative of f ( x ) = cos x as follows. f ′ ( x ) = d d x ( cos x ) = − sin x Set f ′ ( x ) = 0 . − sin x = 0 sin x = 0 x = n π , n = 0 , 1 , 2 , ⋯ Find the derivative of g ( x ) = sin x as follows. g ′ ( x ) = d d x ( sin x ) = cos x Set g ′ ( x ) = 0 . cos x = 0 x = ( 2 n + 1 ) π 2 , n = 0 , 1 , 2 , ⋯ Make a table to find the relative maximum and minimum

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 12.3, Problem 71E

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Whether the statement “The function f(x)=cosx has a relative minimum at a point x=a where g(x)=sinx” is true or false; explain if it is true, and give an example if it is false.

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Chapter 12.3, Problem 70E

Chapter 12.3, Problem 72E

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Chapter 12 Solutions

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

Ch. 12.1 - Prob. 1CQ Ch. 12.1 - Prob. 2CQ Ch. 12.1 - Prob. 3CQ Ch. 12.1 - In Exercises 14, express the angle shown in the...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E

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Whether the statement “The function f ( x ) = cos x has a relative minimum at a point x = a where g ( x ) = sin x ” is true or false; explain if it is true, and give an example if it is false.

Solution Summary: The author explains whether the statement "The function f(x)=mathrmcosx" is true or false, and gives an example if it is false.

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Whether the statement “The function f(x)=cosx has a relative minimum at a point x=a where g(x)=sinx” is true or false; explain if it is true, and give an example if it is false.

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Chapter 12 Solutions