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Solving multiple questions on the application of derivatives

Please show all work.
1. Consider the function
a) Determine the critical points. (Apply the quotient rule carefully to find derivative.)

b) For what intervals in the domain of f is the function increasing?

c) For what intervals in the domain of f is the function decreasing?

2. Find all maximum and minimum values of the function .

3. The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function:


a) Determine the marginal cost function.

4. Determine the derivatives of the following functions:


5. The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is one possible model.

Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm in dollars of this reduction. Government clean-air subsidies amount ot $500 per pound of pollutanat removed. How many pounds of pollutant should the firm remove each day in order to minimize the net cost (cost - subsidy)?

6. Suppose that during a prolonged recession, property values depreciated 2% every six months. If a house originally cost $180000, determine its value at the end of five years.

7. Suppose you want to be earning an annual salary of $80000 in 10 years. You have been offered a job with a guaranteed 5% increase in salary per year. The initial salary is negotiable. What initial salary should you request to meet your goal of $80k in 10 years?


Solution Summary

The solution gives detailed steps on solving multiple questions on the application of derivatives. All formula, rules and calculations are shown and explained.