Solving multiple questions on the application of derivatives
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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:
dollars
a) Determine the marginal cost function.
4. Determine the derivatives of the following functions:
a)
b)
c)
d)
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?
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