Preface 

ix  
Introduction 

1  (2) 


3  (63) 

Functions and Their Graphs 


3  (15) 


18  (9) 


27  (5) 

Zeros of FunctionsThe Quadratic Formula and Factoring 


32  (8) 

Exponents and Power Functions 


40  (8) 

Functions and Graphs in Applications 


48  (18) 

Graphing Functions Using Technology 


60  (6) 


66  (71) 

The Slope of a Straight Line 


68  (11) 

The Slope of a Curve at a Point 


79  (6) 


85  (9) 

Limits and the Derivative 


94  (10) 

Differentiability and Continuity 


104  (6) 

Some Rules for Differentiation 


110  (7) 


117  (4) 

The Derivative as a Rate of Change 


121  (16) 

Applications of the Derivative 


137  (72) 

Describing Graphs of Functions 


137  (12) 

The First and Second Derivative Rules 


149  (10) 

Curve Sketching (Introduction) 


159  (7) 

Curve Sketching (Conclusion) 


166  (7) 


173  (10) 

Further Optimization Problems 


183  (10) 

Applications of Derivatives to Business and Economics 


193  (16) 

Techniques of Differentiation 


209  (29) 

The Product and Quotient Rules 


209  (9) 

The Chain Rule and the General Power Rule 


218  (6) 

Implicit Differentiation and Related Rates 


224  (14) 


238  (30) 


238  (4) 

The Exponential Function ex 


242  (5) 

Differentiation of Exponential Functions 


247  (6) 

The Natural Logarithm Function 


253  (5) 


258  (4) 

Properties of the Natural Logarithm Function 


262  (6) 

Applications of the Exponential and Natural Logarithm Functions 


268  (40) 

Exponential Growth and Decay 


268  (11) 


279  (7) 

Applications of the Natural Logarithm Function to Economics 


286  (8) 

Further Exponential Models 


294  (14) 


308  (77) 


309  (9) 


318  (9) 

Definite Integrals and the Fundamental Theorem 


327  (12) 


339  (10) 

Applications of the Definite Integral 


349  (9) 

Techniques of Integration 


358  (9) 


367  (7) 

Applications of Calculus to Probability 


374  (11) 

Functions of Several Variables 


385  (63) 

Examples of Functions of Several Variables 


385  (7) 


392  (9) 

Maxima and Minima of Functions of Several Variables 


401  (9) 

Lagrange Multipliers and Constrained Optimization 


410  (10) 

The Method of Least Squares 


420  (7) 


427  (13) 


440  (8) 

The Trigonometric Functions 


448  


448  (4) 


452  (8) 

Differentiation and Integration of sin t and cos t 


460  (10) 

The Tangent and Other Trigonometric Functions 


470  
Appendix A: Calculus and the TI82 Calculator 

1  (5) 
Appendix B: Calculus and the TI83/TI83 Plus Calculators 

6  (5) 
Appendix C: Calculus and the TI85 Calculator 

11  (5) 
Appendix D: Calculus and the TI86 Calculator 

16  (5) 
Answers to Exercises 

21  
Index 

1  