INSTRUCTOR’S RESOURCE AND
SOLUTIONS MANUAL
CHRISTI VERITY
CALCULUS WITH APPLICATIONS AND
CALCULUS WITH APPLICATIONS ,
BRIEF V ERSION
TWELFTH EDITION
Margaret L. Lial
American River College
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Kent State University
with the Assistance of
Katherine Ritchey Blain Patterson
University of Mount Union
Virginia Military Institute
Sarah Ritchey Patterson
Virginia Military Institute
,Please contact https://support.pearson.com/getsupport/s/ with any queries on this content.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential
damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
Copyright © 2022, 2016, 2012 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All
Rights Reserved. Manufactured in the United States of America. This publication is protected by copyright, and
permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,
or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For
information regarding permissions, request forms, and the appropriate contacts within the Pearson Education Global
Rights and Permissions department, please visit www.pearsoned.com/permissions/.
ISBN-10: 0-13-597462-3
ISBN-13: 978-0-13-597462-9
,CONTENTS
PREFACE ........................................................................................................................................................................ ix
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS.................................................................................. xi
PRETESTS .....................................................................................................................................................................xix
ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
FINAL EXAMINATIONS ...........................................................................................................................................xxix
ANSWERS TO FINAL EXAMINATIONS ................................................................................................................. xliii
SOLUTIONS TO ALL EXERCISES
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials..........................................................................................................................................................1
R.2 Factoring ..............................................................................................................................................................3
R.3 Rational Expressions ........................................................................................................................................... 4
R.4 Equations .............................................................................................................................................................8
R.5 Inequalities .........................................................................................................................................................14
R.6 Exponents...........................................................................................................................................................24
R.7 Radicals..............................................................................................................................................................28
CHAPTER 1 LINEAR FUNCTIONS
1.1 Slopes and Equations of Lines ............................................................................................................................33
1.2 Linear Functions and Applications .....................................................................................................................46
1.3 The Least Squares Line.......................................................................................................................................54
Chapter 1 Review Exercises .......................................................................................................................................66
Extended Application: Predicting Life Expectancy ....................................................................................................74
Copyright © 2022 Pearson Education, Inc. iii
, 2.1 Properties of Functions .......................................................................................................................................77
2.2 Quadratic Functions; Translation and Reflection................................................................................................86
2.3 Polynomial and Rational Functions ..................................................................................................................102
2.4 Exponential Functions ...................................................................................................................................... 115
2.5 Logarithmic Functions ...................................................................................................................................... 125
2.6 Applications: Growth and Decay; Mathematics of Finance ..............................................................................137
Chapter 2 Review Exercises .....................................................................................................................................146
Extended Application: Power Functions ..................................................................................................................162
CHAPTER 3 THE DERIVATIVE
3.1 Limits ...............................................................................................................................................................163
3.2 Continuity .........................................................................................................................................................177
3.3 Rates of Change ................................................................................................................................................184
3.4 Definition of the Derivative ..............................................................................................................................195
3.5 Graphical Differentiation .................................................................................................................................. 219
Chapter 3 Review Exercises .....................................................................................................................................223
Extended Application: A Model for Drugs Administered Intravenously.................................................................. 235
CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives ..................................................................................................................237
4.2 Derivatives of Products and Quotients ..............................................................................................................247
4.3 The Chain Rule .................................................................................................................................................258
4.4 Derivatives of Exponential Functions ...............................................................................................................269
4.5 Derivatives of Logarithmic Functions ..............................................................................................................283
Chapter 4 Review Exercises .....................................................................................................................................296
Extended Application: Electric Potential and Electric Field .....................................................................................308
5.1 Increasing and Decreasing Functions ...............................................................................................................309
5.2 Relative Extrema ..............................................................................................................................................324
5.3 Higher Derivatives, Concavity, and the Second Derivative Test ......................................................................339
5.4 Curve Sketching ...............................................................................................................................................362
Chapter 5 Review Exercises .....................................................................................................................................383
Extended Application: A Drug Concentration Model for Orally Administered Medications ...................................400
SOLUTIONS MANUAL
CHRISTI VERITY
CALCULUS WITH APPLICATIONS AND
CALCULUS WITH APPLICATIONS ,
BRIEF V ERSION
TWELFTH EDITION
Margaret L. Lial
American River College
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Kent State University
with the Assistance of
Katherine Ritchey Blain Patterson
University of Mount Union
Virginia Military Institute
Sarah Ritchey Patterson
Virginia Military Institute
,Please contact https://support.pearson.com/getsupport/s/ with any queries on this content.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential
damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
Copyright © 2022, 2016, 2012 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All
Rights Reserved. Manufactured in the United States of America. This publication is protected by copyright, and
permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,
or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For
information regarding permissions, request forms, and the appropriate contacts within the Pearson Education Global
Rights and Permissions department, please visit www.pearsoned.com/permissions/.
ISBN-10: 0-13-597462-3
ISBN-13: 978-0-13-597462-9
,CONTENTS
PREFACE ........................................................................................................................................................................ ix
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS.................................................................................. xi
PRETESTS .....................................................................................................................................................................xix
ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
FINAL EXAMINATIONS ...........................................................................................................................................xxix
ANSWERS TO FINAL EXAMINATIONS ................................................................................................................. xliii
SOLUTIONS TO ALL EXERCISES
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials..........................................................................................................................................................1
R.2 Factoring ..............................................................................................................................................................3
R.3 Rational Expressions ........................................................................................................................................... 4
R.4 Equations .............................................................................................................................................................8
R.5 Inequalities .........................................................................................................................................................14
R.6 Exponents...........................................................................................................................................................24
R.7 Radicals..............................................................................................................................................................28
CHAPTER 1 LINEAR FUNCTIONS
1.1 Slopes and Equations of Lines ............................................................................................................................33
1.2 Linear Functions and Applications .....................................................................................................................46
1.3 The Least Squares Line.......................................................................................................................................54
Chapter 1 Review Exercises .......................................................................................................................................66
Extended Application: Predicting Life Expectancy ....................................................................................................74
Copyright © 2022 Pearson Education, Inc. iii
, 2.1 Properties of Functions .......................................................................................................................................77
2.2 Quadratic Functions; Translation and Reflection................................................................................................86
2.3 Polynomial and Rational Functions ..................................................................................................................102
2.4 Exponential Functions ...................................................................................................................................... 115
2.5 Logarithmic Functions ...................................................................................................................................... 125
2.6 Applications: Growth and Decay; Mathematics of Finance ..............................................................................137
Chapter 2 Review Exercises .....................................................................................................................................146
Extended Application: Power Functions ..................................................................................................................162
CHAPTER 3 THE DERIVATIVE
3.1 Limits ...............................................................................................................................................................163
3.2 Continuity .........................................................................................................................................................177
3.3 Rates of Change ................................................................................................................................................184
3.4 Definition of the Derivative ..............................................................................................................................195
3.5 Graphical Differentiation .................................................................................................................................. 219
Chapter 3 Review Exercises .....................................................................................................................................223
Extended Application: A Model for Drugs Administered Intravenously.................................................................. 235
CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives ..................................................................................................................237
4.2 Derivatives of Products and Quotients ..............................................................................................................247
4.3 The Chain Rule .................................................................................................................................................258
4.4 Derivatives of Exponential Functions ...............................................................................................................269
4.5 Derivatives of Logarithmic Functions ..............................................................................................................283
Chapter 4 Review Exercises .....................................................................................................................................296
Extended Application: Electric Potential and Electric Field .....................................................................................308
5.1 Increasing and Decreasing Functions ...............................................................................................................309
5.2 Relative Extrema ..............................................................................................................................................324
5.3 Higher Derivatives, Concavity, and the Second Derivative Test ......................................................................339
5.4 Curve Sketching ...............................................................................................................................................362
Chapter 5 Review Exercises .....................................................................................................................................383
Extended Application: A Drug Concentration Model for Orally Administered Medications ...................................400
