
Functions, Graphs, and Models 


1  (94) 


2  (12) 


14  (15) 


29  (11) 

Slope and Linear Functions 


40  (16) 


56  (18) 

Mathematical Modeling and Curve Fitting 


74  (21) 


86  (3) 


89  (2) 

Extended Technology Application The Ecological Effect of Global Warming 


91  (4) 


95  (90) 

Limits and Continuity: Numerically and Graphically 


96  (13) 


109  (5) 


114  (10) 

Differentiation Using Limits of Difference Quotients 


124  (14) 

Differentiation Techniques: The Power and SumDifference Rules 


138  (11) 

Instantaneous Rates of Change; Business Applications 


149  (9) 

Differentiation Techniques: The Product and Quotient Rules 


158  (8) 


166  (8) 


174  (11) 


178  (10) 


188  

Extended Technology Application Path of a Baseball: The Tale of the Tape 


181  (4) 

Applications of Differentiation 


185  (100) 

Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs 


186  (16) 

Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs 


202  (14) 

Graph Sketching: Asymptotes and Rational Functions 


216  (18) 

Using Derivatives to Find Absolute Maximum and Minimum Values 


234  (15) 

MaximumMinimum Problems: Business and Economics Applications 


249  (17) 


266  (7) 

Implicit Differentiation and Related Rates 


273  (12) 


279  (2) 


281  (2) 

Extended Technology Application Maximum Sustainable Harvest 


283  (2) 

Exponential and Logarithmic Functions 


285  (78) 


286  (14) 


300  (17) 

Applications: The Uninhibited Growth Model, dP/dt = kP 


317  (15) 


332  (13) 

The Derivatives of ax and loga X 


345  (5) 

An Economics Application: Elasticity of Demand 


350  (13) 


356  (2) 


358  (2) 

Extended Technology Application The Business of MotionPicture BoxOffice Revenue 


360  (3) 


363  (70) 


364  (9) 

Area and Definite Integrals 


373  (14) 

Limits of Sums and Accumulations 


387  (13) 

Properties of Definite Integrals 


400  (8) 

Integration Techniques: Substitution 


408  (6) 

Integration Techniques: Integration by Parts 


414  (8) 

Integration Techniques: Tables 


422  (11) 


428  (1) 


429  (2) 

Extended Technology Application Total Sales of SherwinWilliams, Intel, Sprint, and The Gap 


431  (2) 

Applications of Integration 


433  (62) 

An Economics Application: Consumer's Surplus and Producer's Surplus 


434  (6) 

Applications of the Models ∫ To Poekt dt and ∫ To Poekt dt 


440  (8) 


448  (6) 


454  (11) 

Probability: Expected Value; The Normal Distribution 


465  (12) 


477  (3) 


480  (15) 


489  (2) 


491  (2) 

Extended Technology Application Curve Fitting and the Volume of a Bottle of Soda 


493  (2) 

Functions of Several Variables 


495  (54) 

Functions of Several Variables 


496  (7) 


503  (6) 

HigherOrder Partial Derivatives 


509  (3) 

MaximumMinimum Problems 


512  (11) 

An Application: The LeastSquares Technique 


523  (8) 

Constrained Maximum and Minimum Values: Lagrange Multipliers 


531  (8) 


539  (10) 


543  (2) 


545  (1) 

Extended Technology Application Minimizing Employees' Travel Time in a Building 


546  (3) 
Cumulative Review 

549  (4) 
Appendix: Review of Basic Algebra 

553  (16) 



Table 1 Integration Formulas 


567  (2) 

Table 2 Areas for a Standard Normal Distribution 


569  
Answers 

A1  
Index 

I1  