Explanation Given: The cost-benefit curve for pollution control is given by the function y = 9.2 x 106 − x ( 0 ≤ x ≤ 100 ) . Here, y represent the cost in thousands of dollars, and removing x percent of a specified pollutant. 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 If the f ( x ) = u ( x ) v ( x ) , if all indicated derivatives exist, and v ( x ) ≠ 0 , then the derivative of the function f ( x ) by division rule is, f ′ ( x ) = v ( x ) ⋅ u ′ ( x ) − u ( x ) ⋅ v ′ ( x ) ( v ( x ) ) 2 Calculation: Consider the cost benefit curve. y = 9.2 x 106 − x ( 0 ≤ x ≤ 100 ) . The steps of calculating local extrema in TI83 calculator is given below: Step 1: Press ON button and then press Y= button. Step 2: Then, enter the function Y = 9.2 x 106 − x . Step 3: Now, press window button and set the window as X min = 0 , X max = 100 , X s c l = 10 , Y min = − 20 , Y max = 120 and Y s c l = 10 . Step 4: Press GRAPH button, to get the graph. It displays the graph as; From the graph, one can conclude that the function has no critical point and thus, no extrema exist. Thus, there is no local extrema. Consider the function y = 9.2 x 106 − x . Now, differentiate the above function with respect to x, to get; y ′ = d d x ( 9

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 12.6, Problem 34E

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To calculate: The approximate location of all local extrema and points of inflection of the function y=9.2x106−x with the help of graphing calculator.

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Chapter 12.6, Problem 33E

Chapter 12.6, Problem 35E

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 approximate location of all local extrema and points of inflection of the function y = 9.2 x 106 − x with the help of graphing calculator.

Solution Summary: The author calculates the cost-benefit curve for pollution control with the help of graphing calculator.

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To calculate: The approximate location of all local extrema and points of inflection of the function y=9.2x106−x with the help of graphing calculator.

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Chapter 12 Solutions