Exam 4: Techniques of Differentiation With Applications

A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.4 cm/day. How fast is the area growing when the culture is 3 centimeters in radius? (The area of a disc of radius r is .)

According to the equation given, a toy manufacturer calculates its daily profit P (in dollars)based on the number of workers n it employs. Calculate the marginal product at an employment level of 100 workers.

Find the indicated derivative. Please round the answer to the nearest hundredth.

Find using implicit differentiation.

Compute the derivative.

The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months? Enter your answer in dollars/month rounded to the nearest cent and without the units.

Calculate . You need not expand your answer.

Given. Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the following function.

Find the derivative of the function.

The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 30,000 CDs per day and .

Given. Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________

The cost, in thousands of dollars, of airing x television commercials during a Super Bowl game is given by the formula . Estimate how fast (in dollars per television commercial)the cost is going up when x = 8.

Use logarithmic differentiation to find .

Find the equation of the line tangent to the graph of the given function at the point with .

Find using implicit differentiation.

Assume that the demand function for tuna in a small coastal town is given by where p is the price (in dollars)per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in 1 month. Calculate the price that the town s fishery should charge for tuna in order to produce a demand of 625 pounds of tuna per month.

Find the derivative of the function.