Preface 

ix  
Introduction 

1  (2) 


3  (67) 

Functions and Their Graphs 


3  (15) 


18  (9) 


27  (7) 

Zeros of FunctionsThe Quadratic Formula and Factoring 


34  (8) 

Exponents and Power Functions 


42  (7) 

Functions and Graphs in Applications 


49  (21) 

Graphing Functions Using Technology 


62  (6) 


68  (2) 


70  (74) 

The Slope of a Straight Line 


72  (11) 

The Slope of a Curve at a Point 


83  (6) 


89  (12) 

Limits and the Derivative 


101  (10) 

Differentiability and Continuity 


111  (5) 

Some Rules for Differentiation 


116  (7) 


123  (5) 

The Derivative as a Rate of Change 


128  (16) 


143  (1) 

Applications of the Derivative 


144  (70) 

Describing Graphs of Functions 


144  (12) 

The First and Second Derivative Rules 


156  (10) 

Curve Sketching (Introduction) 


166  (7) 

Curve Sketching (Conclusion) 


173  (7) 


180  (9) 

Further Optimization Problems 


189  (9) 

Applications of Derivatives to Business and Economics 


198  (16) 


213  (1) 

Techniques of Differentiation 


214  (29) 

The Product and Quotient Rules 


214  (8) 

The Chain Rule and the General Power Rule 


222  (6) 

Implicit Differentiation and Related Rates 


228  (15) 


242  (1) 

The Exponential and Natural Logarithm Functions 


243  (31) 


243  (4) 

The Exponential Function ex 


247  (5) 

Differentiation of Exponential Functions 


252  (5) 

The Natural Logarithm Function 


257  (5) 


262  (4) 

Properties of the Natural Logarithm Function 


266  (8) 


272  (2) 

Applications of the Exponential and Natural Logarithm Functions 


274  (39) 

Exponential Growth and Decay 


274  (10) 


284  (8) 

Applications of the Natural Logarithm Function to Economics 


292  (6) 

Further Exponential Models 


298  (15) 


312  (1) 


313  (76) 


314  (9) 


323  (9) 

Definite Integrals and the Fundamental Theorem 


332  (12) 


344  (10) 

Applications of the Definite Integral 


354  (9) 

Techniques of Integration 


363  (9) 


372  (7) 

Applications of Calculus to Probability 


379  (10) 


388  (1) 

Functions of Several Variables 


389  (63) 

Examples of Functions of Several Variables 


389  (7) 


396  (9) 

Maxima and Minima of Functions of Several Variables 


405  (8) 

Lagrange Multipliers and Constrained Optimization 


413  (11) 

The Method of Least Squares 


424  (7) 


431  (12) 


443  (9) 


451  (1) 

The Trigonometric Functions 


452  (1) 


452  (4) 


456  (8) 

Differentiation and Integration of sin t and cos t 


464  (10) 

The Tangent and Other Trigonometric Functions 


474  (7) 


481  
Appendix A: Calculus and the TI82 Calculator 

A1  
Appendix B: Calculus and the TI83/TI83 Plus Calculators 

A5  
Appendix C: Calculus and the TI85 Calculator 

A9  
Appendix D: Calculus and the TI86 Calculator 

A13  
Answers to Exercises 

A19  
Index 

I1  