Explanation Result used: Second-derivative Test for Absolute Extrema on an Interval: Let f ( x ) be a continuous on an interval I from a to b with only one critical number c in ( a , b ) . If f ′ ( c ) = 0 and f ″ ( x ) > 0 , then f ( c ) is the absolute minimum of f on I . If f ′ ( c ) = 0 and f ″ ( x ) < 0 , then f ( c ) is a absolute maximum of f on I . Calculation: The given function is f ( x ) = 8 − x 4 . Since every polynomial function is continuous function on real numbers. The function f ( x ) = 8 − x 4 is continuous function on real number. Obtain the critical points of the function. The derivative of the function is computed as follows, f ′ ( x ) = d d x ( 8 − x 4 ) = d d x ( 8 ) − d d x ( x 4 ) = 0 − ( 4 x 3 ) = − 4 x 3 Thus, the derivative of the function is f ′ ( x ) = − 4 x 3 . The critical point x such that f ′ ( x ) = 0 . − 4 x 3 = 0 x = 0 Therefore, the critical point of the function is x = 0

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 4.5, Problem 34E

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To find: The absolute extremum of the f(x)=8−x4.

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Chapter 4.5, Problem 33E

Chapter 4.5, Problem 35E

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Chapter 4 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 4.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 ...Ch. 4.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 4 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 5 Find the critical numbers of f,...Ch. 4.1 - Prob. 6MP Ch. 4.1 - Matched Problem 7 Given f(x) = x3 9x2 + 24x 10,...Ch. 4.1 - Matched Problem 8 The graph in Figure 13...Ch. 4.1 - Matched Problem 9 The graph of the total revenue...Ch. 4.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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The absolute extremum of the f ( x ) = 8 − x 4 .

Solution Summary: The author calculates the absolute extremum of the function f(x)=8-x 4. Since every polynomial function is continuous function on real numbers, the derivative of

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Chapter 4 Solutions