INSTRUCTOR’S RESOURCE AND
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SOLUTIONS MANUAL
CHRISTI VERITY
d
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C ALCULUS WITH A PPLICATIONS AND
C ALCULUS WITH A PPLICATIONS ,
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B RIEF V ERSION
TWELFTH EDITION
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Margaret L. Lial
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American River College
Raymond N. Greenwell
47
Hofstra University
Nathan P. Ritchey
Kent State University
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with the Assistance of
Katherine Ritchey Blain Patterson
University of Mount Union
??
Virginia Military Institute
Sarah Ritchey Patterson
Virginia Military Institute
??
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, CONTENTS
PREFACE................................................................................................................................................................... ix
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HINTS FOR TEACHING CALCULUS WITH APPLICATIONS ............................................................................ xi
PRETESTS ................................................................................................................................................................. xix
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ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
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FINAL EXAMINATIONS ......................................................................................................................................... xxix
ANSWERS TO FINAL EXAMINATIONS............................................................................................................... xliii
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SOLUTIONS TO ALL EXERCISES
CHAPTER R ALGEBRA REFERENCE
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R.1 Polynomials .................................................................................................................................................. 1
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R.2 Factoring ....................................................................................................................................................... 3
R.3 Rational Expressions .................................................................................................................................... 4
R.4 Equations ...................................................................................................................................................... 8
47
R.5 Inequalities ................................................................................................................................................... 14
R.6 Exponents ..................................................................................................................................................... 24
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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
, CHAPTER 2 NONLINEAR FUNCTIONS
2.1 Properties of Functions.................................................................................................................................. 77
2.2 Quadratic Functions; Translation and Reflection .......................................................................................... 86
2.3 Polynomial and Rational Functions .............................................................................................................. 102
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2.4 Exponential Functions ................................................................................................................................... 115
2.5 Logarithmic Functions .................................................................................................................................. 125
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2.6 Applications: Growth and Decay; Mathematics of Finance .......................................................................... 137
Chapter 2 Review Exercises.................................................................................................................................. 146
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Extended Application: Power Functions ............................................................................................................... 162
CHAPTER 3 THE DERIVATIVE
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3.1 Limits ............................................................................................................................................................ 163
3.2 Continuity...................................................................................................................................................... 177
3.3 Rates of Change ............................................................................................................................................ 184
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3.4 Definition of the Derivative .......................................................................................................................... 195
3.5 Graphical Differentiation .............................................................................................................................. 219
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Chapter 3 Review Exercises.................................................................................................................................. 223
Extended Application: A Model for Drugs Administered Intravenously .............................................................. 235
47
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
??
? ?
iv Copyright © 2022 Pearson Education, Inc. CONTENTS
, CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................................ 309
5.2 Relative Extrema ........................................................................................................................................... 324
5.3 Higher Derivatives, Concavity, and the Second Derivative Test .................................................................. 339
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5.4 Curve Sketching ............................................................................................................................... 362
Chapter 5 Review Exercises.................................................................................................................................. 383
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Extended Application: A Drug Concentration Model for Orally Administered Medications ............................... 400
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CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................................... 401
6.2 Applications of Extrema................................................................................................................................ 411
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6.3 Further Business Applications....................................................................................................................... 432
6.4 Implicit Differentiation ................................................................................................................................. 440
6.5 Related Rates ................................................................................................................................................. 457
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6.6 Differentials: Linear Approximation ............................................................................................................. 466
Chapter 6 Review Exercises.................................................................................................................................. 472
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Extended Application: A Total Cost Model for a Training Program .................................................................... 483
CHAPTER 7 INTEGRATION
47
7.1 Antiderivatives .............................................................................................................................................. 485
7.2 Substitution ................................................................................................................................................... 497
7.3 Area and the Definite Integral ....................................................................................................................... 507
??
7.4 The Fundamental Theorem of Calculus ........................................................................................................ 521
7.5 The Area Between Two Curves .................................................................................................................... 538
7.6 Numerical Integration ................................................................................................................................... 556
??
Chapter 7 Review Exercises.................................................................................................................................. 570
Extended Application: Estimating Depletion Dates for Minerals ......................................................................... 588
??
? ?
CONTENTS Copyright © 2022 Pearson Education, Inc. v
tu
SOLUTIONS MANUAL
CHRISTI VERITY
d
yg
C ALCULUS WITH A PPLICATIONS AND
C ALCULUS WITH A PPLICATIONS ,
en
B RIEF V ERSION
TWELFTH EDITION
iu
Margaret L. Lial
s2
American River College
Raymond N. Greenwell
47
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
??
? ?
, CONTENTS
PREFACE................................................................................................................................................................... ix
tu
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS ............................................................................ xi
PRETESTS ................................................................................................................................................................. xix
d
ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
yg
FINAL EXAMINATIONS ......................................................................................................................................... xxix
ANSWERS TO FINAL EXAMINATIONS............................................................................................................... xliii
en
SOLUTIONS TO ALL EXERCISES
CHAPTER R ALGEBRA REFERENCE
iu
R.1 Polynomials .................................................................................................................................................. 1
s2
R.2 Factoring ....................................................................................................................................................... 3
R.3 Rational Expressions .................................................................................................................................... 4
R.4 Equations ...................................................................................................................................................... 8
47
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
, CHAPTER 2 NONLINEAR FUNCTIONS
2.1 Properties of Functions.................................................................................................................................. 77
2.2 Quadratic Functions; Translation and Reflection .......................................................................................... 86
2.3 Polynomial and Rational Functions .............................................................................................................. 102
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2.4 Exponential Functions ................................................................................................................................... 115
2.5 Logarithmic Functions .................................................................................................................................. 125
d
2.6 Applications: Growth and Decay; Mathematics of Finance .......................................................................... 137
Chapter 2 Review Exercises.................................................................................................................................. 146
yg
Extended Application: Power Functions ............................................................................................................... 162
CHAPTER 3 THE DERIVATIVE
en
3.1 Limits ............................................................................................................................................................ 163
3.2 Continuity...................................................................................................................................................... 177
3.3 Rates of Change ............................................................................................................................................ 184
iu
3.4 Definition of the Derivative .......................................................................................................................... 195
3.5 Graphical Differentiation .............................................................................................................................. 219
s2
Chapter 3 Review Exercises.................................................................................................................................. 223
Extended Application: A Model for Drugs Administered Intravenously .............................................................. 235
47
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
??
? ?
iv Copyright © 2022 Pearson Education, Inc. CONTENTS
, CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................................ 309
5.2 Relative Extrema ........................................................................................................................................... 324
5.3 Higher Derivatives, Concavity, and the Second Derivative Test .................................................................. 339
tu
5.4 Curve Sketching ............................................................................................................................... 362
Chapter 5 Review Exercises.................................................................................................................................. 383
d
Extended Application: A Drug Concentration Model for Orally Administered Medications ............................... 400
yg
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................................... 401
6.2 Applications of Extrema................................................................................................................................ 411
en
6.3 Further Business Applications....................................................................................................................... 432
6.4 Implicit Differentiation ................................................................................................................................. 440
6.5 Related Rates ................................................................................................................................................. 457
iu
6.6 Differentials: Linear Approximation ............................................................................................................. 466
Chapter 6 Review Exercises.................................................................................................................................. 472
s2
Extended Application: A Total Cost Model for a Training Program .................................................................... 483
CHAPTER 7 INTEGRATION
47
7.1 Antiderivatives .............................................................................................................................................. 485
7.2 Substitution ................................................................................................................................................... 497
7.3 Area and the Definite Integral ....................................................................................................................... 507
??
7.4 The Fundamental Theorem of Calculus ........................................................................................................ 521
7.5 The Area Between Two Curves .................................................................................................................... 538
7.6 Numerical Integration ................................................................................................................................... 556
??
Chapter 7 Review Exercises.................................................................................................................................. 570
Extended Application: Estimating Depletion Dates for Minerals ......................................................................... 588
??
? ?
CONTENTS Copyright © 2022 Pearson Education, Inc. v
