Explanation Given Information: The percentage of unemployed workers in service occupations can be modeled by: p ( x ) = − 0039 x 3 + 0.594 x 2 − 1.967 x + 7.555 where x is the number of years since 2003 . Formula used: The concept of Max-Min Principle-1 is taken into consideration which is as follows: Suppose f is a continuous function defined over a closed interval [ a , b ] . To find the absolute maximum and minimum values over [ a , b ] : First find f ' ( x ) Determine all critical values in [ a , b ] . That is, find all c in [ a , b ] for which f ' ( c ) = 0 or f ' ( c ) does not exist. List the values from the previous step and endpoints of the interval: a , c 1 , c 2 , .. , c n , b . Evaluate f ( x ) for each value above: f ( a ) , f ( c 1 ) , f ( c 2 ) , ... f ( c n ) , f ( b ) . The largest of them is the absolute maximum of f over [ a , b ] . The smallest of these is the absolute minimum of f over [ a , b ] . Calculation: Consider the provided function, p ( x ) = − 0039 x 3 + 0.594 x 2 − 1.967 x + 7.555. The attention is restricted to the years 2003 to 2013 . Therefore, values of x are to be taken as: 0 ≤ x ≤ 10 . In order to find when the percentage of unemployed workers was maximum, find p ' ( x ) first: p ' ( x ) = − 0.117 x 2 + 1.188 x − 1.9767. Find the critical values. p ' ( x ) exists for all values of real numbers, so solve the equation below to obtain the values of x . p ' ( x ) = 0 − 0.117 x 2 + 1.188 x − 1.967 = 0 Use the quadratic formula to solve the above equation, x = − ( 1

Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133862386

Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent

Publisher: PEARSON

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Chapter 2.4, Problem 99E

To determine

To calculate: The year during the period 2003−2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by:

p(x)=−0039x3+0.594x2−1.967x+7.555,

where x is the number of years since 2003.

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Chapter 2.4, Problem 98E

Chapter 2.4, Problem 100E

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The year during the period 2003 − 2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by: p ( x ) = − 0039 x 3 + 0.594 x 2 − 1.967 x + 7.555 , where x is the number of years since 2003 .

Solution Summary: The author explains how the maximum percentage of unemployed workers in service occupations occurred in underset_2011

To calculate: The year during the period 2003−2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by:

p(x)=−0039x3+0.594x2−1.967x+7.555,

where x is the number of years since 2003.

Want to see the full answer?

Chapter 2 Solutions

Additional Math Textbook Solutions

The year during the period 2003 − 2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by: p ( x ) = − 0039 x 3 + 0.594 x 2 − 1.967 x + 7.555 , where x is the number of years since 2003 .

Solution Summary: The author explains how the maximum percentage of unemployed workers in service occupations occurred in underset_2011

To calculate: The year during the period 2003−2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by: p(x)=−0039x3+0.594x2−1.967x+7.555, where x is the number of years since 2003.

Want to see the full answer?

Chapter 2 Solutions

Additional Math Textbook Solutions

To calculate: The year during the period 2003−2013 was the percentage of unemployed workers in service occupations maximum when the percentage of unemployed workers in service occupations can be modeled by:

p(x)=−0039x3+0.594x2−1.967x+7.555,

where x is the number of years since 2003.