Exam 10: Derivatives

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find the marginal revenue at and tell what it predicts about the sale of the next unit. Round your answer to two decimal places. ​

If ​ and , find . ​

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

Use a table utility with x-values larger than 10,000 to investigate . What does the table indicate about ? ​ ​

A certain calling card costs 6.8 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 68 cent connection fee. If is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. ​

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. ​ ​

Suppose that the revenue function for a certain product is given by , where x is in thousands of units and R is in thousands of dollars. Find the marginal revenue (in thousands of dollars per unit) when 4,000 units are sold. Round your answer to two decimal places. ​

If the revenue for a product (in dollars) is and the average revenue per unit is , , find . ​

Suppose the total revenue function for a blender is where x is the number of units sold. What function gives the marginal revenue? ​

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Decide whether the sale of the 100st cell phone or the 700st brings in more revenue. ​ ​

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

Graph the marginal profit function for the profit function where P(x) is in dollars and x is the number of units. What level of production and sales will give a zero marginal profit? ​

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. Is more revenue expected from the 101st unit sold or from the 401st unit sold? ​

Find and simplify. ​

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

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

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find . Round your answer to two decimal places. ​

Find the indicated derivative and simplify. ​ for ​

A graph of is shown and a c-value is given. For this problem, use the graph to find . ​ ​ ​

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find , and explain what this value represents. Round your answer to two decimal places. ​