CALCULUS
                                 IN
                      BUSINESSANDECONOMICS
                               G. S. Monk
                              Mathematics 112
                             Revised Winter 2010
                        Published by Professional Copy & Print
                              1414 NE42ndSt.
                              Seattle, WA 98105
                              (206-634-2689)
               c
        Copyright !1981 by G.S. Monk. All rights reserved.
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                                    Contents
                                    Preface                                                                                                                                                                                                                            v
                                    1TangentsandDerivedGraphs                                                                                                                                                                                                          1
                                                          Worksheet #1. The Vertical Speed of a Shell . . . . . . . . . . . . . . . ......                                                                                                                             2
                                                          Worksheet #2. Two Versions of Marginal Revenue and Cost                                                                                            . . . . . . ...... 7
                                                          Worksheet #3. Tangents and Secants . . . . . . . . . . . . . . . . . . . . . .... 12
                                                          Worksheet #4. Drawing Speed Graphs . . . . . . . . . . . . . . . . . . . . . ... 18
                                                          Worksheet #5. Drawing and Using a Marginal Revenue Graph . . . . ....... 22
                                                          Worksheet #6. Derived Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26
                                    2        Tangents and Formulas; The Derivative                                                                                                                                                                                  33
                                                          Worksheet #7. The Formula for the Slope of the Tangent                                                                                    .    .   .   .    .   .    ........ 34
                                                          Worksheet #8. The Formulas for Two Speed Graphs . . . . . . . . . . . ...... 40
                                                          Worksheet #9. Taking Derivatives                                                     .    .   .   .    .   .    .   .    .   .   .    .   .    .   .   .    .   .    .   .   .    .   .... 45
                                                          Worksheet #10. Using the Marginal Revenue and Marginal Cost Formulas . . . . .                                                                                                                            51
                                                          Worksheet #11. Two Balloons . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                                       55
                                    3DifferentiationTechnique                                                                                                                                                                                                       61
                                                          Worksheet #12. A Second Set of Rules . . . . . . . . . . . . . . . . . . . . . . .. 62
                                                          Worksheet #13. Combining Differentiation Rules . . . . . . . . . . . ....... 68
                                    4Optimization                                                                                                                                                                                                                   73
                                                          Worksheet #14. Local and Global Optima . . . . . . . . . . . . . . . . . . .... 74
                                                          Worksheet #15. Demand Curves . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                                        79
                                                          Worksheet #16. The Second Derivative Test . . . . . . . . . . . . . . . ...... 82
                                    5FunctionsofSeveralVariables                                                                                                                                                                                                    89
                                                          Worksheet #17. Multivariable Functions . . . . . . . . . . . . . . . . ....... 90
                                                          Worksheet #18. Linear Programming . . . . . . . . . . . . . . . . . . . . . .... 97
                                    6        GoingBackwards: Integration                                                                                                                                                                                         103
                                                          Worksheet #19. Distances from Speed Graphs . . . . . . . . . . . . . . ......104
                                                          Worksheet #20. Total Revenue and Cost from Marginal Revenue and Cost . . . . . 111
                                                          Worksheet #21. Area Under Graphs . . . . . . . . . . . . . . . . . . . . . . . ..117
                                                                                                                                                     iii
       iv                                CONTENTS
          Worksheet #22. Areas by Formula . . . . . . . . . . . . . . . . . . . . . . . . ..126
          Worksheet #23. Anti-Derivatives . . . . . . . . . . . . . . . . . . . . . . .....130
          Worksheet #24. The Fundamental Theorem of Integral Calculus ..........136
       Appendices
          Answers to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . ...143
          Graphs and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163