Exam 10: Derivatives

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Is the marginal revenue greater at 800 cell phones or at 1000? ​ ​

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

Complete the table and use it to predict the limit, if it exists. ​ ​ ​

Differentiate the given function. ​ ​

This problem contains a function and its graph, where . Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically. ​ ​ ​

Calculate the derivative of the function with the appropriate formula. ​ ​

Suppose that the cost function for a commodity is dollars. Find the marginal cost at units and tell what this predicts about the cost of producing 1 additional unit. Round your answer to two decimal places. ​

Graph the function using a window with and . What does the graph indicate about ​ ​

Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists. ​

For the function given, find ​ ​

Suppose that the cost function for a commodity is dollars. Calculate to find the actual cost of producing the 4th unit. Round your answer to two decimal places. ​

Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at . ​

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

Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A to B, B to C, and A to C from smallest to greatest. ​ ​

For the given function, find the instantaneous rate of change at . A graphing utility's numerical derivative feature may be used to check your work. ​ ​

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 for all values of t?

For the function in this problem, find the derivative, by using the definition. ​ ​

Find the derivative of the function. ​ ​

Find the derivative at the given x-value with the appropriate rule. ​ ​

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