Exam 10: Derivatives

The revenue (in thousands of dollars) from the sale of a product is , where x is the number of units sold. At what rate is the marginal revenue changing when the number of units being sold is 35? Round your answer to four decimal places. ​

Find the derivative of the function. ​ ​

Total revenue is in dollars and x is the number of units. Suppose that in a monopoly market, the demand function for a product is given by , where x is the number of units and p is the price in dollars. Find the total revenue from the sale of 200 units. ​

Suppose that for selected years from 1970 to 2006, the following table shows the percent of total U.S. workers who are female. ​ ​ Assume these data can be modeled with the function where p(t) is the percent of the U.S. workforce that is female and t is the number of years past 1970. Find the instantaneous rate of change in 2000 and 2006 by using the function that models the instantaneous rate of change of the percent of U.S. workers who are female. Round your answer to three decimal places. ​

Suppose that the proportion P of voters who recognize a candidate's name t months after the start of the campaign is given by . Find the rate of change of P when and explain its meaning. ​

Find the indicated derivative and simplify. ​ for ​

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce? ​ ​

If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by ​ , ​ Find the rate of change of C with respect to p.

Use properties of limits and algebraic methods to find the limit, if it exists. ​ ​

Use the graph of and the given c-value to find . ​ ​ ​

Suppose that the total cost function, in dollars, for a certain commodity is given by , where x is the number of units produced. Find the instantaneous rate of change of the average cost for any level of production. ​

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function ​ . ​ What is the monthly charge if 1,100 kWh of electricity is consumed in a month? Round your answer to two decimal places. ​

For the function given, find all x-values where . ​ ​

If the profit function for a product is given by , find . ​

For the function given, find all x-values where f (x) has a local maximum point. ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

Use the graph of and the given c-value to find . ​ ​ ​

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. Is this function continuous at

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce? ​ ​

If and , find . ​