To determine To calculate: The absolute maximum or minimum of the given function f ( x ) = 1 − x 3 + x . Explanation Given: The function, f ( x ) = 1 − x 3 + x in interval [ 0 , 3 ] . Formula used: If f ( x ) = u ( x ) v ( x ) , if all indicated derivatives exist, and if v ( x ) ≠ 0 , then f ′ ( x ) = v ( x ) ⋅ u ′ ( x ) − u ( x ) ⋅ v ′ ( x ) [ v ( x ) ] 2 Calculation: According to the extreme-value theorem, and it needs to consider only the critical numbers of f ( x ) and the endpoints. Endpoints are 0 and 3 . Now, find the derivative and determine the critical numbers: f ' ( x ) = ( 3 + x ) ( − 1 ) − ( 1 − x ) ( 1 )

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 12E

To determine

To calculate: The absolute maximum or minimum of the given function f(x)=1−x3+x.

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Chapter 12.3, Problem 11E

Chapter 12.3, Problem 13E

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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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