Explanation Let f ( x ) = p x 2 + q x + r With p ≠ 0 and consider the interval [ a , b ] . then f ' ( x ) = 2 p x + q , and by the MVT f ' ( c ) = f ( 4 ) − f ( 0 ) 4 − 0 Because c > 0 , f ' ( c ) ≤ 3 , so f ( 4 ) − f ( 0 ) ≤ 12 .finally, f ( 4 ) ≤ f ( 0 ) + 12 = 14...

3rd Edition

ISBN: 9781464114885

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 4.3, Problem 69E

To determine

Suppose that $f (0) = 2 and f' (x) \leq 3 for x > 0$ that the MVT interval $[0, 4]$ to prove that $f (4) \leq 14.$

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Chapter 4.3, Problem 68E

Chapter 4.3, Problem 70E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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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Knowledge Booster

Suppose that f ( 0 ) = 2 and f ' ( x ) ≤ 3 for x &gt; 0 that the MVT interval [ 0 , 4 ] to prove that f ( 4 ) ≤ 14.

Suppose that f(0)=2 and f'(x)≤3 for x>0 that the MVT interval [0,4] to prove that f(4)≤14.

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Chapter 4 Solutions

Suppose that f ( 0 ) = 2 and f ' ( x ) ≤ 3 for x > 0 that the MVT interval [ 0 , 4 ] to prove that f ( 4 ) ≤ 14.

Suppose that $f (0) = 2 and f' (x) \leq 3 for x > 0$ that the MVT interval $[0, 4]$ to prove that $f (4) \leq 14.$