Explanation Let h ( x ) = f ( x ) − g ( x ) h ' ( x ) = f ' ( x ) − g ' ( x ) f ' ( x ) ≤ g ' ( x ) x ≥ 0 , h ' ( x ) ≤ 0 a n d x ≥ 0 h ( 0 ) = f ( 0 ) − g ( 0 ) = 0 h ( x ) ≤ 0 x ≥ o As

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.3, Problem 64E

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Prove that if f(0)=g(0) and f'(x)≤g'(x) for x≥0, then f(x)≤g(x) for all x≥0 show that the function given by y=f(x)−g(x)

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Chapter 4.3, Problem 63E

Chapter 4.3, Problem 65E

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ 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 Ch. 4.1 - Prob. 6E

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Prove that if f ( 0 ) = g ( 0 ) a n d f ' ( x ) ≤ g ' ( x ) f o r x ≥ 0 , t h e n f ( x ) ≤ g ( x ) f o r a l l x ≥ 0 show that the function given by y = f ( x ) − g ( x )

Solution Summary: The author explains that the function given by y=f(x)-g can be used to determine that if h is no increasing is cannot climb above zero.

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Prove that if f(0)=g(0) and f'(x)≤g'(x) for x≥0, then f(x)≤g(x) for all x≥0 show that the function given by y=f(x)−g(x)

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Chapter 4 Solutions