Explanation Given: The function is y = x 2 + 1 x − 4 and the interval is [ 5 , 6 ] Calculation: The minimum and maximum values of a function occur at the critical points or end points. Given a function f ( x ) , a number c in the domain if the function is said to be a critical point if either f ' ( c ) = 0 or f ' ( c ) does not exist. Consider the function y = f ( x ) = x 2 + 1 x − 4 on [ 5 , 6 ] . To find the critical points of this function, differentiate it and equate it to zero and find the roots. f ( x ) = x 2 + 1 x − 4 f ' ( x ) = 2 x ( x − 4 ) − ( x 2 + 1 ) ( 1 − 0 ) ( x − 4 ) 2 f ' ( x ) = 2 x 2 − 8 x − x 2 − 1 ( x − 4 ) 2 f ' ( x ) = x 2 − 8 x − 1 ( x − 4 ) 2 Equate f ' ( x ) to zero then we get that, f ' ( x ) = x 2 − 8 x − 1 ( x − 4 ) 2 = 0 x 2 − 8 x − 1 = 0 x = 4 ± 17 x = 4 + 17 ≈ 8

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.2, Problem 35E

To determine

To find:

The minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.

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Chapter 4.2, Problem 34E

Chapter 4.2, Problem 36E

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Chapter 4 Solutions

CALCULUS (CLOTH)

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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The minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.

Solution Summary: The author calculates the minimum and maximum values of a function on the given interval by comparing values at the critical points and endpoints.

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To find: The minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.

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Chapter 4 Solutions

To find:

The minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.