To determine To calculate: Absolute maximum or minimum of given function f ( x ) = x 4 − 18 x 2 + 1 . Explanation Given: Function f ( x ) = x 4 − 18 x 2 + 1 , interval [ − 4 , 4 ] . Formula used: If f ( x ) = x n then; f ′ ( x ) = n x n − 1 Calculation: According to the extreme-value theorem, it needs to consider only the critical numbers of f ( x ) and the endpoints. Endpoints are − 4 and 4 . Now find the derivative and determine the critical numbers: f ( x ) = x 4 − 18 x 2 + 1 f ' ( x ) = 0 4 x 3 − 36 x = 0 4 x ( x 3 − 9 ) = 0 </

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 12.3, Problem 9E

To determine

To calculate: Absolute maximum or minimum of given function f(x)=x4−18x2+1.

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Chapter 12.3, Problem 8E

Chapter 12.3, Problem 10E

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Chapter 12 Solutions

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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