Explanation Given: The provided function is: f ( x ) = x 2 / 5 + 3 . Formula used: Write the formula for derivative of power rule. If f ( x ) = x n for any number n , then the derivative. f ′ ( x ) = n x n − 1 If f ( x ) = k for any real number k , then the derivative is defined by the formula. f ′ ( x ) = 0 Calculation: Consider the provided equation: f ( x ) = x 2 / 5 + 3 …… (1) Differentiating the function with respect to x . f ′ ( x ) = 2 5 x 2 5 − 1 + 0 = 2 5 x − 3 / 5 …… (2) Calculate the critical point by equating f ′ ( x ) equal to zero. Substitute 0 for f ′ ( x ) . 2 5 x − 3 / 5 = 0 Solve for x . x = 0 The critical point is only one at x = 0 . Hence, there may be two test point: x = − 1 and, x = 1 Substitute − 1 for x in equation (2)

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 12.1, Problem 30E

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To calculate: The location of local extremum of the function f(x)=x2/5+3.

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Chapter 12.1, Problem 29E

Chapter 12.1, Problem 31E

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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The location of local extremum of the function f ( x ) = x 2 / 5 + 3 .

Solution Summary: The author calculates the location of local extremum of the function f(x) = 2/5+3.

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To calculate: The location of local extremum of the function f(x)=x2/5+3.

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Chapter 12 Solutions