Table of Contents

PREFACE		ix
1	PROBLEM SOLVING, FUNCTIONS AND MODELS	1
Introduction   1
1.0   The Process of Problem Solving   2
1.1   Functions   14
1.2   Mathematical Models and Formulation from Verbal Descriptions   42
1.3   Linear Functions and Models   70
1.4   Functions with One Concavity: Quadratic, Exponential, Power   105
1.5   Functions with Changing Concavity: Cubic, Quartic, Logistic   131
Summary   153
2	RATES OF CHANGE	155
Introduction   155
2.1   Average and Percent Rate of Change Over an Interval   157
2.2   Instantaneous Rate of Change at a Point   176
2.3   Derivative Notation and Interpretation, Marginal Analysis   200
2.4   The Algebraic Definition of Derivative and Basic Derivative Rules   218
2.5   Composite Functions and the Chain Rule   244
2.6   The Product Rule   263
Summary   277
3	SINGLE-VARIABLE OPTIMIZATION AND ANALYSIS	280
Introduction   280
3.1   Analysis of Graphs and Slope Graphs   282
3.2   Optimization - Algebraic Determination of Maxima and Minima   303
3.3   Testing of Critical Points, Concavity, and Points of Inflection   322
3.4   Post-Optimality Analysis   349
3.5*   Percent Rate of Change at a Point, Elasticity, Average Cost   387
Summary   415
4	CONTINUOUS PROBABILITY AND INTEGRATION	418
Introduction   418
4.1   Continuous Probability Distributions   421
4.2   Approximating Area under Curves (Subinterval Methods)   439
4.3   Finding Exact Areas Using Limits of Sums   465
4.4   Recovering Functions from their Derivatives   472
4.5   The Fundamental Theorem of Calculus   493
4.6   Variable Limits of Integration and Medians, Improper Integrals   511
4.7*   Consumer and Producer Surplus   523
Summary   536
APPENDIX A   MATHEMATICAL DETAILS		541
APPENDIX B   STUDENT-GENERATED PROJECTS		547
APPENDIX C   ANSWERS TO SELECTED EXERCISES		A-1
INDEX		I-1