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Work on your computer to solve the following problems. Type your answer and calculations in the space after each question. The spaces expand as you...

Please see attached for business calculus

Module 08 Written Assignment Instructions In this assignment, you will want to demonstrate the application of not only the first derivative, but  also the second derivative to solving important applications in business. Work on your computer to solve the following problems. Type your answer and calculations in the  space after each question.  The spaces expand as you work.  For full credit on each problem,  you must show both your  answer  (final solution) plus your  calculations.  Keep your typing simple.  For example, you may use x^n to mean x to the nth power and sqrt(x) for the square root of x. Be  very careful with large fractions and consider using grouping symbols very liberally. Guess and  check or trial and error methods are not acceptable. 6 points per problem, #4 is worth 8. Problems 1. Find the critical points for f(x) = x 5  – 4x 3  + 10. 2. Construct a sign chart for the derivative. Then determine the relative and absolute  extrema for y = -4x 2  + 4 on the interval [-3,3]. 3. Based on data from 1995 to 1999, the number of employees in the printing and publishing  industry may be modeled by E ( t )= −4.417 t 3   + 24.93 t 2   − 25.30 +1450 thousand employees, where  is the number of  years since 1995. (Source: Modeled from  Statistical Abstract of the United States, 2001 , Table 979, p. 622.) According to the model, when did the industry have its maximum and minimum number of  employees? How many people were employed at these times? 4. Gatorade/Tropicana North America, a subsidiary of PepsiCo, produces fruit juices and 
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Module 08 Written Assignment other flavored beverages. Based on data from 1999 to 2001, the net sales (revenue) of  Gatorade/Tropicana North America may be modeled by R(t)=107t 2 +496t+3452 million dollars  and the operating profit (earnings before interest and taxes) may be modeled by P(t) = −18.5t 2  + 85.5t + 433 million dollars, where t is the number of years since 1999. (Source: Modeled from 2001 PepsiCo Annual Report, p.44.) a) In what year are net sales projected to reach a maximum? b) Find the cost function for Gatorade/Tropicana North America. c) According to the model, in what year are costs expected to reach a maximum? d) Compare the results of (a) and (c). Do the results seem reasonable? 5. Use the second derivative to determine the point of inflection for y = x 3  – x 2  – 8x + 12. 6. Use the second derivative to determine where the maximum and minimum rates of  change occur for a vehicle’s speed modeled by the function v(t) = 0.0591t 3  - 0.3399t 2  + 0.5019t + 0.00594, where t is the time in minutes after leaving  a stoplight. Copyright ©2011 Rasmussen College
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Module 08 Written Assignment
Instructions
In this assignment, you will want to demonstrate the application of not only the first derivative, but also the second derivative to solving important...

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