Review Exercises for
Applied Calculus
Finite Mathematics & Applied Calculus
Topic: Introduction to the Derivative

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Question 1 Let f be the function specified by following table.

x-2-1012
f(x)52125


Question 2 The number of network managers in the US over the years 1989-2001 followed the curve

where t is time in years (t = 0 represents 1980).

* Source: Bureau of Labor Statistics via Economy.com, Tech Target/New York Times, August 8, 2001, p. G1.

(a) Compute the average rate of change of N over the intervals [10, 15] and [15, 20].

(b)Interpret the results of part (a).

(c) The rate of change of N is   over the given period 1989-2001.


Question 3 The annual profit of Lotus Development Corp. for the years 1990-1994 are shown in the following chart. (Losses are shown as negative.)

During which one-year interval was the average rate of change of annual profits

† Figures are approximate. Source: Datastream: Company Reports/The New York Times, Jun 6, 1995, p. D8.


Question 4 The demand for Gauss Jordan sneakers is given by

where p is the price in dollars per pair and q is the monthly sales of said sneakers by Sammy Sporting Authority.

(a) Complete the following table, rounding all anwers to two decimal places.

(b) Estimate both q(120) and q'(120). Interpret your results. (Round all answers to the nearest whole number.)  


Question 5 Look carefully at each of the graphs below, and select the corect answers for each graph.

The slope of the tangent is 0 at the point

The slope of the tangent is 2 at the point

The slope of the tangent is -1 at the point

 

The slope of the tangent is 0 at the points

The slope of the tangent is 1 at the point

The slope of the tangent is -1 at the point

 


Question 6   Annual sales of Eli Lilly Corp.'s human growth hormone Humatrope can be modeled by

where S(t) represents annual sales in millions of dollars, and t represents the number of years since the drug's approval by the FDA in 1987.*

* The model is a very crude one, based on 1991 sales data, total sales data through May, 1992 and very rough estimates of the potential market and selling price. Source: Senate Judiciary Committee; Subcommittee on Antitrust and Monopoly/The New York Times, May 14, 1992, p. D1.


Question 7 Calculate the derivative of the following functions algebraically.
Note You should enter the answers using computer formula notation -- e.g. enter 3x-2 as 3*x^(-2)


Question 8 The weekly cost of manufacturing x pairs of Gauss-Jordan Sneakers is

(a) What is the marginal cost at a sales level of 1000 pairs per week?

(b) What is the average cost per pair at a sales level of 1000 pairs per week?

(c) At the above sales level, the marginal cost is increasing
decreasing
at a rate of $ per pair.    

(d) At the above sales level, the marginal cost is greater than
Approximately equal to    
less than
the average cost.

(e) In general, if the marginal cost is increasing, and there is no fixed cost, then the marginal cost is greater than
Approximately equal to    
less than
the average cost.


We would welcome submissions of additional questions to add to this page. Submit questions with answers to:

Stefan Waner
(matszw@hofstra.edu)

Steven R. Costenoble
(matsrc@hofstra.edu)

Last Updated:October, 2001

Copyright © 1999 StefanWaner and Steven R. Costenoble

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