R. Functions, Graphs, and Models

R.1 Graphs and Equations

R.2 Functions and Models

R.3 Finding Domain and Range

R.4 Slope and Linear Functions

R.5 Nonlinear Functions and Models

R.6 Mathematical Modeling and Curve Fitting

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application Average Price of a Movie Ticket

1. Differentiation

1.1 Limits: A Numerical and Graphical Approach

1.2 Algebraic Limits and Continuity

1.3 Average Rates of Change

1.4 Differentiation Using Limits of Difference Quotients

1.5 The Power and Sum—Difference Rules

1.6 The Product and Quotient Rules

1.7 The Chain Rule

1.8 Higher-Order Derivatives

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

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

2. Applications of Differentiation

2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs

2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs

2.3 Graph Sketching: Asymptotes and Rational Functions

2.4 Using Derivatives to Find Absolute Maximum and Minimum Values

2.5 Maximum—Minimum Problems; Business, Economics, and General Applications

2.6 Marginals and Differentials

2.7 Elasticity of Demand

2.8 Implicit Differentiation and Related Rates

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application–Maximum Sustainable Harvest

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Applications: Uninhibited and Limited Growth Models

3.4 Applications: Decay

3.5 The Derivatives of a^x and log_a x

3.6 A Business Application: Amortization

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application–The Business of Motion Picture Revenue and DVD Release

4. Integration

4.1 Antidifferentiation

4.2 Antiderivatives as Areas

4.3 Area and Definite Integrals

4.4 Properties of Definite Integrals

4.5 Integration Techniques: Substitution

4.6 Integration Techniques: Integration by Parts

4.7 Integration Techniques: Tables

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application–Business: Distribution of Wealth

5. Applications of Integration

5.1 Consumer Surplus and Producer Surplus

5.2 Integrating Growth and Decay Models

5.3 Improper Integrals

5.4 Probability

5.5 Probability: Expected Value; The Normal Distribution

5.6 Volume

5.7 Differential Equations

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application–Curve Fitting and Volumes of Containers

6. Functions of Several Variables

6.1 Functions of Several Variables

6.2 Partial Derivatives

6.3 Maximum—Minimum Problems

6.4 An Application: The Least-Squares Technique

6.5 Constrained Optimization

6.6 Double Integrals

   Chapter Summary

   Chapter Review Exercises

   Chapter Test

   Extended Technology Application–Minimizing Employees’ Travel Time in a Building

Cumulative Revi

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

About this Textbook

• An intuitive approach to introducing the concepts builds on students’ earlier mathematical experience or a new experience presented by the authors before the concept is formalized. The writing style addresses students in a direct, down-to-earth manner.
• The accessible, visual presentation helps students to navigate easily through the book. Artwork and figures are an integral part of the intuitive introductions to calculus concepts.
• Algebra diagnostic and review material is available for students who need to strengthen their basic skills.
  • Prerequisite Skills Diagnostic Test at the beginning of the text gives a convenient way to assess strengths and weaknesses. Answers at the back of the book direct students to the appropriate algebra remediation sections within the text.
  • Algebra review is provided at two levels: Appendix A addresses the basics, while Chapter R addresses functions, graphs, and models.
• Exponential and log functions are presented later (in Chapter 3), allowing students to focus more directly on the development of the derivative in Chapters 1 and 2 while using polynomial functions.
• Section support features give students the help they need without getting in the way.
  • Objectives are listed at the beginning of each section, providing a roadmap of the material ahead.
  • Quick Check exercises after examples provide students with a way to check understanding at key junctures in the section.
  • Section Summaries help students pull together the key ideas of the section prior to working the exercises. These appear just prior to exercise sets.
• Abundant section exercises give students the practice they need to understand and master the concepts. Exercises address basic skills and build conceptual understanding through a variety of exercise types including skills, applications, synthesis problems, thinking/writing exercises, and technology connection exercises.
• Technology is integrated but optional. The text allows for the utilization of graphing calculators, spreadsheets, and smartphone applications. All technology is clearly labeled and can be omitted as needs dictate.
  • Technology Connection features are designed with three distinct purposes: 1) learn a concept using technology, 2) check or verify a solution using technology, or 3) investigate a topic using technology.
  • Technology Connections Exercises are clearly labeled with an icon.
  • Extended Technology Applications at the end of the chapter provide a motivational context for students to apply what they’ve learned. These can be done individually or in a group setting.
• Test preparation material at the end of every chapter is designed to help students excel on tests.
  • Chapter Summaries are redesigned to be more reference-like, helping students distill key ideas and prepare for tests.
  • Chapter Review exercises feature Concept Reinforcement, Review Exercises, and Synthesis Exercises. All exercises are keyed back to specific sections in the chapter to guide students towards assistance (and to help instructors in making assignments).
  • Chapter Tests are designed to mirror the tests typically administered in class.
• Applications are grouped by discipline within the exercise sets, organized under the headings of Business/Economics, Life/Physical Science, Social Science, and General Interest, to show stu

New and updated features

• Applications are a major focus of this revision, in particular, applications for business.
  • Additional coverage of exponential functions has been added to Section R.5 to support use of these functions in applications.
  • The former Section 3.6 “An Economics Application: Elasticity of Demand” has been moved to Section 2.7 so students get to the application sooner and can use the concept throughout Chapter 3.
  • A discussion of annuities has been added to Section 3.5, and a new section dedicated to amortization (using Excel as an option) has been added as a new Section 3.6.
  • Applications have been updated to reflect more current data and trends whenever possible.
• Exercise sets have been carefully evaluated to ensure appropriate gradation of level, odd/even pairing and specific connection to the objectives being evaluated. In addition, MyMathLab usage data was analyzed to expose any exercises that needed improvements.

Content Updates

• Chapter R: Several new exercises have been added to this chapter including ten in R.2 addressing how to describe functions verbally and translate them algebraically. In R.5, a subsection and several exercises were added covering exponential functions and their graphs to help bridge the gap on student understanding of exponential functions. In R.6, more discussion of exponential functions was added along with four new exercises involving exponential models. Throughout, data-driven examples were updated when possible.
• Chapter 1: The goal for Chapter 1 was to update the data-based examples and consolidate similar exercises into a more manageable number. Section 1.8 has the greatest change with the addition of examples and exercises designed to help students visualize acceleration and velocity. In addition, L’Hopital’s Rule is briefly covered in a synthesis exercise.
• Chapter 2: In Section 2.5, Example 3 has been rewritten to factor in cost, spreadsheet use has been added to show how numerical min/max can be found, a new Technology Connection has been added, and Examples 6 and 7 were integrated into a single example. Several examples in Section 2.6 have been consolidated and a new Quick Check exercise has been added. The main change to Chapter 2 is the addition of an expanded and updated Section 2.7 Elasticity. This new location is a more natural fit than its former position as Section 3.6. The former 2.7 Implicit Differentiation and Related Rates has become Section 2.8.
• Chapter 3: New material on exponential functions has been added to Section 3.1 based on the expanded content in R.5. In Section 3.2, there is more emphasis on the general antiderivative for 1/x, for all x except x = 0, through additional examples and exercises. The Rule of 70 is now included in Section 3.3 as well as a new Technology Connection. Section 3.5 has been expanded to include a discussion on annuities. New Section 3.6 covers the topic of amortization and includes some Excel spreadsheet applications.
• Chapter 4: Application examples and exercises were added and updated throughout Chapter 4. In addition, new material on Simpson’s Rule was added to Section 4.2 and the topic of Recursion was moved to a synthesis exercise in Section 4.6.
• Chapter 5: Topics throughout Chapter 5 were expanded, allowing for over 80 new exercises and applications. Improper integration at a vertical asymptote was added to Section 5.3 and volume of shells was added to Section 5.6. Section 5.6 “Volume” was expanded to include some discussion using shells, and 6.4 “The Least-Squares Technique” was expanded to include a derivation of an exponential regression by hand.
• Chapter 6: The main change in Chapter 6 is that exponential regression was added to Section 6.4 and average value of a two-variable func