Explanation Given: The function of total revenue for Proctor & Gamble Company for the year 2010 to 2015 is, R ( x ) = − 1.1 x 2 + 27 x − 81 Here, x is the number corresponds to the year. If x = 10 , the year would be 2010. 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 To find local maximum and minimum find the values of x from the equation f ′ ( x ) = 0 . Then find f ″ ( x ) and put the values of x. If f ″ ( x ) equals some positive quantity then it will be Local minimum is located at that point x and if f ″ ( x ) equals some negative quantity then Local maximum is located at the point at that point. Calculation: Recall the expression of R ( x ) . R ( x ) = − 1.1 x 2 + 27 x − 81 Differentiate the function with respect to x by using the power rule of the derivative. R ′ ( x ) = − 1.1 ( 2 x 2 − 1 ) + 27 ( 1 ) − 0 = − 2.2 x + 27 …… (1) Calculate the critical point by equating R ′ ( x ) equal to zero

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 52E

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To calculate: The year at which the local maximum revenue occurs in the interval (2010,2015) for Proctor & Gamble Company.

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Chapter 12.1, Problem 54E

Chapter 12.1, Problem 53E

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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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The year at which the local maximum revenue occurs in the interval ( 2010 , 2015 ) for Proctor & Gamble Company.

Solution Summary: The author explains how to calculate the local maximum revenue for Proctor & Gamble Company for the year 2010 to 2015 by using the power rule of the derivative.

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To calculate: The year at which the local maximum revenue occurs in the interval (2010,2015) for Proctor & Gamble Company.

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The year at which the local maximum revenue occurs in the interval ( 2010 , 2015 ) for Proctor &amp; Gamble Company.

Solution Summary: The author explains how to calculate the local maximum revenue for Proctor & Gamble Company for the year 2010 to 2015 by using the power rule of the derivative.

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To calculate: The year at which the local maximum revenue occurs in the interval (2010,2015) for Proctor & Gamble Company.

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Chapter 12 Solutions

The year at which the local maximum revenue occurs in the interval ( 2010 , 2015 ) for Proctor & Gamble Company.