To determine To calculate: The absolute extrema of provided function f ( x ) = ( x 2 + 4 ) 1 3 ; [ − 1 , 2 ] on the given interval. Explanation Given: The provided function is f ( x ) = ( x 2 + 4 ) 1 3 ; [ − 1 , 2 ] . Formula used: The property of derivative as; d d x ( x n ) = n x n − 1 And Extreme value theorem If a function f ( x ) is continuous on a closed interval [ a , b ] and has only one critical number in the interval [ a , b ] , say, x = c . Then, f ( x ) has both absolute maxima and absolute minima in the given interval occurring either at an endpoint of [ a , b ] or at the critical number x = c . Calculation: According to the extreme-value theorem, we need consider only the critical numbers of f and the endpoints, -1 and 2, of the interval. Begin by finding the derivative and determining the critical numbers: f ' ( x ) = 1 3 ( x 2 + 4 ) 1 3 − 1 ⋅ d d x [

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

12th Edition

ISBN: 9780135998304

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

Publisher: PEARSON

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Chapter 12.3, Problem 16E

To determine

To calculate: The absolute extrema of provided function f(x) = (x2 + 4)13; [−1, 2] on the given interval.

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Chapter 12.3, Problem 15E

Chapter 12.3, Problem 17E

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Chapter 12 Solutions

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (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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