Exam 10: Derivatives

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. ​ at ​

For the function in this problem, approximate by using the numerical derivative feature of a graphing utility. ​ ​

For the function in this problem, approximate by computing with . Round your answer to four decimal places. ​ ​

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 . Is C continuous at ? ​

A certain calling card costs 6.3 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 63 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. ​ ​

Differentiate the given function. ​ ​

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​ ​

Identify x-values where has a maximum point or a minimum point, where is increasing, and where is decreasing. ​ ​

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 function that models the instantaneous rate of change of the percent of U.S. workers who are female. ​

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

Find and . ​ and ​

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

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

Use analytic methods to find the limit as for the given function. ​ ​

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 . Is C continuous at ?

Find the second derivative. ​ ​

The graph of a company's profit function is shown. For the given problem, use the graph to answer the following questions about points A, B, and C. Rank from smallest to largest the marginal profit at these points. ​ ​

If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is . What is the acceleration of the object when ? ​

Differentiate the given function. ​ ​

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. ​ ​