Explanation Given: The equality f ( 0 ) = g ( 0 ) and inequality f ′ ( x ) ≤ g ′ ( x ) holds true for x ≥ 0 . Concept used: Assume f be a differentiable function on an open interval ( a , b ) then f is increasing on ( a , b ) if f ′ ( x ) > 0 for x ∈ ( a , b ) and f is decreasing on ( a , b ) if f ′ ( x ) < 0 for x ∈ ( a , b ) . Calculation: Assume the function h ( x ) as follows. h ( x ) = f ( x ) − g ( x ) ...... (1) Differentiate the above equation (1) with respect to x as follows. h ′ ( x ) = d ( f ( x ) − g ( x ) ) d x = f ′ ( x ) − g ′ ( x ) It is given that the inequality f ′ ( x ) ≤ g ′ ( x ) holds true for x ≥ 0 . Therefore, h ′ ( x ) ≤ 0 for all x ≥ 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.3, Problem 73E

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The inequality f(x)≤g(x) for all x≥0 is true.

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Chapter 4.3, Problem 72E

Chapter 4.3, Problem 74E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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