To determine To calculate: The absolute extrema of provided function f ( x ) = ( x 2 + 18 ) 2 / 3 ; [ − 3 , 2 ] on the given interval. Explanation Given: The provided function is f ( x ) = ( x 2 + 18 ) 2 / 3 ; [ − 3 , 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 ( x ) and the endpoints, -3 and 2, of the interval

12th Edition

ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12.3, Problem 15E

To determine

To calculate: The absolute extrema of provided function f(x) = (x2 + 18)2/3 ; [−3, 2] on the given interval.

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Chapter 12.3, Problem 14E

Chapter 12.3, Problem 16E

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