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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Question

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

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

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Prob. 18E Ch. 4.4 - Prob. 19E Ch. 4.4 - Prob. 20E Ch. 4.4 - Prob. 21E Ch. 4.4 - Prob. 22E Ch. 4.4 - Prob. 23E Ch. 4.4 - Prob. 24E Ch. 4.4 - Prob. 25E Ch. 4.4 - Prob. 26E Ch. 4.4 - Prob. 27E Ch. 4.4 - Prob. 28E Ch. 4.4 - Prob. 29E Ch. 4.4 - Prob. 30E Ch. 4.4 - Prob. 31E Ch. 4.4 - Prob. 32E Ch. 4.4 - Prob. 33E Ch. 4.4 - Prob. 34E Ch. 4.4 - Prob. 35E Ch. 4.4 - Prob. 36E Ch. 4.4 - Prob. 37E Ch. 4.4 - Prob. 38E Ch. 4.4 - Prob. 39E Ch. 4.4 - Prob. 40E Ch. 4.4 - Prob. 41E Ch. 4.4 - Prob. 42E Ch. 4.4 - Prob. 43E Ch. 4.4 - Prob. 44E Ch. 4.4 - Prob. 45E Ch. 4.4 - Prob. 46E Ch. 4.4 - Prob. 47E Ch. 4.4 - Prob. 48E Ch. 4.4 - Prob. 49E Ch. 4.4 - Prob. 50E Ch. 4.4 - Prob. 51E Ch. 4.4 - Prob. 52E Ch. 4.4 - Prob. 53E Ch. 4.4 - Prob. 54E Ch. 4.4 - Prob. 55E Ch. 4.4 - Prob. 56E Ch. 4.4 - Prob. 57E Ch. 4.4 - Prob. 58E Ch. 4.4 - Prob. 59E Ch. 4.4 - Prob. 60E Ch. 4.4 - Prob. 61E Ch. 4.4 - Prob. 62E Ch. 4.5 - Prob. 1PQ Ch. 4.5 - Prob. 2PQ Ch. 4.5 - Prob. 3PQ Ch. 4.5 - Prob. 1E Ch. 4.5 - Prob. 2E Ch. 4.5 - Prob. 3E Ch. 4.5 - Prob. 4E Ch. 4.5 - Prob. 5E Ch. 4.5 - Prob. 6E Ch. 4.5 - Prob. 7E Ch. 4.5 - Prob. 8E Ch. 4.5 - Prob. 9E Ch. 4.5 - Prob. 10E Ch. 4.5 - Prob. 11E Ch. 4.5 - Prob. 12E Ch. 4.5 - Prob. 13E Ch. 4.5 - Prob. 14E Ch. 4.5 - Prob. 15E Ch. 4.5 - Prob. 16E Ch. 4.5 - Prob. 17E Ch. 4.5 - Prob. 18E Ch. 4.5 - Prob. 19E Ch. 4.5 - Prob. 20E Ch. 4.5 - Prob. 21E Ch. 4.5 - Prob. 22E Ch. 4.5 - Prob. 23E Ch. 4.5 - Prob. 24E Ch. 4.5 - Prob. 25E Ch. 4.5 - Prob. 26E Ch. 4.5 - Prob. 27E Ch. 4.5 - Prob. 28E Ch. 4.5 - Prob. 29E Ch. 4.5 - Prob. 30E Ch. 4.5 - Prob. 31E Ch. 4.5 - Prob. 32E Ch. 4.5 - Prob. 33E Ch. 4.5 - Prob. 34E Ch. 4.5 - Prob. 35E Ch. 4.5 - Prob. 36E Ch. 4.5 - Prob. 37E Ch. 4.5 - Prob. 38E Ch. 4.5 - Prob. 39E Ch. 4.5 - Prob. 40E Ch. 4.5 - Prob. 41E Ch. 4.5 - Prob. 42E Ch. 4.5 - Prob. 43E Ch. 4.5 - Prob. 44E Ch. 4.5 - Prob. 45E Ch. 4.5 - Prob. 46E Ch. 4.5 - Prob. 47E Ch. 4.5 - Prob. 48E Ch. 4.5 - Prob. 49E Ch. 4.5 - Prob. 50E Ch. 4.5 - Prob. 51E Ch. 4.5 - Prob. 52E Ch. 4.5 - Prob. 53E Ch. 4.5 - Prob. 54E Ch. 4.5 - Prob. 55E Ch. 4.5 - Prob. 56E Ch. 4.5 - Prob. 57E Ch. 4.5 - Prob. 58E Ch. 4.5 - Prob. 59E Ch. 4.5 - Prob. 60E Ch. 4.5 - Prob. 61E Ch. 4.5 - Prob. 62E Ch. 4.5 - Prob. 63E Ch. 4.5 - Prob. 64E Ch. 4.5 - Prob. 65E Ch. 4.5 - Prob. 66E Ch. 4.5 - Prob. 67E Ch. 4.5 - Prob. 68E Ch. 4.5 - Prob. 69E Ch. 4.5 - Prob. 70E Ch. 4.5 - Prob. 71E Ch. 4.5 - Prob. 72E Ch. 4.5 - Prob. 73E Ch. 4.5 - Prob. 74E Ch. 4.5 - Prob. 75E Ch. 4.5 - Prob. 76E Ch. 4.5 - Prob. 77E Ch. 4.5 - Prob. 78E Ch. 4.5 - Prob. 79E Ch. 4.6 - Prob. 1PQ Ch. 4.6 - Prob. 2PQ Ch. 4.6 - Prob. 3PQ Ch. 4.6 - Prob. 1E Ch. 4.6 - Prob. 2E Ch. 4.6 - Prob. 3E Ch. 4.6 - Prob. 4E Ch. 4.6 - Prob. 5E Ch. 4.6 - Prob. 6E Ch. 4.6 - Prob. 7E Ch. 4.6 - Prob. 8E Ch. 4.6 - Prob. 9E Ch. 4.6 - Prob. 10E Ch. 4.6 - Prob. 11E Ch. 4.6 - Prob. 12E Ch. 4.6 - Prob. 13E Ch. 4.6 - Prob. 14E Ch. 4.6 - Prob. 15E Ch. 4.6 - Prob. 16E Ch. 4.6 - Prob. 17E Ch. 4.6 - Prob. 18E Ch. 4.6 - Prob. 19E Ch. 4.6 - Prob. 20E Ch. 4.6 - Prob. 21E Ch. 4.6 - Prob. 22E Ch. 4.6 - Prob. 23E Ch. 4.6 - Prob. 24E Ch. 4.6 - Prob. 25E Ch. 4.6 - Prob. 26E Ch. 4.6 - Prob. 27E Ch. 4.6 - Prob. 28E Ch. 4.6 - Prob. 29E Ch. 4.6 - Prob. 30E Ch. 4.6 - Prob. 31E Ch. 4.6 - Prob. 32E Ch. 4.6 - Prob. 33E Ch. 4.6 - Prob. 34E Ch. 4.6 - Prob. 35E Ch. 4.6 - Prob. 36E Ch. 4.6 - Prob. 37E Ch. 4.6 - Prob. 38E Ch. 4.6 - Prob. 39E Ch. 4.6 - Prob. 40E Ch. 4.6 - Prob. 41E Ch. 4.6 - Prob. 42E Ch. 4.6 - Prob. 43E Ch. 4.6 - Prob. 44E Ch. 4.6 - Prob. 45E Ch. 4.6 - Prob. 46E Ch. 4.6 - Prob. 47E Ch. 4.6 - Prob. 48E Ch. 4.6 - Prob. 49E Ch. 4.6 - Prob. 50E Ch. 4.6 - Prob. 51E Ch. 4.6 - Prob. 52E Ch. 4.6 - Prob. 53E Ch. 4.6 - Prob. 54E Ch. 4.6 - Prob. 55E Ch. 4.6 - Prob. 56E Ch. 4.6 - Prob. 57E Ch. 4.6 - Prob. 58E Ch. 4.6 - Prob. 59E Ch. 4.6 - Prob. 60E Ch. 4.6 - Prob. 61E Ch. 4.6 - Prob. 62E Ch. 4.6 - Prob. 63E Ch. 4.6 - Prob. 64E Ch. 4.6 - Prob. 65E Ch. 4.6 - Prob. 66E Ch. 4.6 - Prob. 67E Ch. 4.6 - 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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.