PREFACE IX

INDEX OF APPLICATIONS XIII

### CHAPTER 1 FUNCTIONS 1

1.1 Functions, Graphs, and Tables, 1

1.2 Graphing Utilities, 9

1.3 Functions and Graphs in Applications, 20

1.4 Linear Functions, 30

1.5 Other Important Functions, 44

1.6 Operations on Functions, 51

### CHAPTER 2 THE DERIVATIVE 59

2.1 The Slope of a Curve at a Point, 59

2.2 The Derivative as a Rate of Change, 69

2.3 The Derivative Function, 83

2.4 Describing Graphs of Functions, 94

2.5 The First and Second Derivative Rules, 108

2.6 Limits and the Derivative, 119

2.7 Differentiability and Continuity, 129

### CHAPTER 3 ALGEBRAIC DIFFERENTIATION AND ITS APPLICATIONS 137

3.1 Some Rules for Differentiation, 137

3.2 More About Derivatives, 145

3.3 Obtaining Graphs of Functions (Introduction), 153

3.4 Obtaining Graphs of Functions (Conclusion), 159

3.5 Optimization Problems, 167

3.6 Further Optimization Problems, 175

3.7 Applications of Calculus to Business and Economics, 185

### CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 195

4.1 The Exponential Function ex , 195

4.2 The Product and Quotient Rules, 204

4.3 The Chain Rule, 212

4.4 The Natural Logarithm Function, 217

4.5 The Derivative of ln x, 223

4.6 Properties of the Natural Logarithm Function, 228

### CHAPTER 5 APPLICATIONS OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS 235

5.1 Exponential Growth and Decay, 236

5.2 Compound Interest, 252

5.3 Applications of the Natural Logarithm Function to Economics, 261

### CHAPTER 6 ANTIDIFFERENTIATION AND DIFFERENTIAL EQUATIONS 271

6.1 Antidifferentiation, 271

6.2 Differential Equations, 280

6.3 Qualitative Theory of Autonomous Differential Equations, 286

6.4 Applications of Autonomous Differential Equations, 296

### CHAPTER 7 THE DEFINITE INTEGRAL 309

7.1 Areas and Riemann Sums, 310

7.2 The Definite Integral, 320

7.3 Areas in the xy-Plane, 331

7.4 Applications of the Definite Integral, 339

7.5 The Fundamental Theorem of Calculus, 348

7.6 Techniques of Integration, 357

7.7 Improper Integrals, 367

7.8 Applications of Calculus to Probability, 374

### CHAPTER 8 FUNCTIONS OF SEVERAL VARIABLES 383

8.1 Examples of Functions of Several Variables, 383

8.2 Partial Derivatives, 391

8.3 Maxima and Minima of Functions of Several Variables, 403

8.4 Lagrange Multipliers and Constrained Optimization, 414

### APPENDICES 427

A Using Visual Calculus Software, 427

B Solving Quadratic Equations, 433

C Using the TI-82 Graphing Calculator: A Summary, 439

D Using the TI-83 Graphing Calculator: A Summary, 446

E Using the TI-85 Graphing Calculator: A Summary, 453

ANSWERS TO ODD-NUMBERED EXERCISES 459

INDEX 483

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