Explanation Let x > 0 is continuous on [ 0 , x ] and differentiable on ( 0 , x ) , the mean value theorem guarantees there exists a c ∈ ( 0 , x ) such that f ' ( c ) = f ( x ) − f ( 0 ) x − 0 or f ( x ) = f

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4, Problem 23CRE

To determine

To find out using the MVT to prove that if f'(x)≤2 for x>0 and f(0)=4, then f(x)≤2x+4 for all x≥0.

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Chapter 4, Problem 22CRE

Chapter 4, Problem 24CRE

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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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To find out using the MVT to prove that if f ' ( x ) ≤ 2 for x > 0 and f ( 0 ) = 4 , then f ( x ) ≤ 2 x + 4 for all x ≥ 0.

Solution Summary: The author explains the solution obtained for the MVT to show that 2x+4.

Concept explainers

Videos

To find out using the MVT to prove that if f'(x)≤2 for x>0 and f(0)=4, then f(x)≤2x+4 for all x≥0.

Want to see the full answer?

Chapter 4 Solutions

To find out using the MVT to prove that if f ' ( x ) ≤ 2 for x &gt; 0 and f ( 0 ) = 4 , then f ( x ) ≤ 2 x + 4 for all x ≥ 0.

Solution Summary: The author explains the solution obtained for the MVT to show that 2x+4.

Concept explainers

Videos

To find out using the MVT to prove that if f'(x)≤2 for x>0 and f(0)=4, then f(x)≤2x+4 for all x≥0.

Want to see the full answer?

Chapter 4 Solutions

To find out using the MVT to prove that if f ' ( x ) ≤ 2 for x > 0 and f ( 0 ) = 4 , then f ( x ) ≤ 2 x + 4 for all x ≥ 0.