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

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.3, Problem 60E

To determine

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 4.3, Problem 59E

Chapter 4.3, Problem 61E

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Chapter 4 Solutions

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

Solution Summary: The author explains that the MVT interval left[0,4right] is used to determine the value of the .

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

Want to see the full answer?

Chapter 4 Solutions

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.

Solution Summary: The author explains that the MVT interval left[0,4right] is used to determine the value of the .

Concept explainers

Videos

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

Want to see the full answer?

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.