INSTRUCTOR’S
SOLUTIONS MANUAL
BEVERLY FUSFIELD
CALCULUS
FOR THE LIFE SCIENCES
SECOND EDITION
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Edinboro University
Margaret L. Lial
American River College
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
,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.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2015 Pearson Education, Inc.
Publishing as Pearson, 75 Arlington Street, Boston, MA 02116.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written
permission of the publisher. Printed in the United States of America.
ISBN-13: 978-0-321-96448-9
ISBN-10: 0-321-96448-9
www.pearsonhighered.com
,CONTENTS
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials ....................................................................................................................................... 1
R.2 Factoring............................................................................................................................................ 3
R.3 Rational Expressions ......................................................................................................................... 4
R.4 Equations ........................................................................................................................................... 7
R.5 Inequalities. ..................................................................................................................................... 11
R.6 Exponents ........................................................................................................................................ 21
R.7 Radicals ........................................................................................................................................... 24
CHAPTER 1 FUNCTIONS
1.1 Lines and Linear Functions ............................................................................................................. 28
1.2 The Least Squares Line ................................................................................................................... 39
1.3 Properties of Functions .................................................................................................................... 46
1.4 Quadratic Functions; Translation and Reflection ............................................................................ 54
1.5 Polynomial and Rational Functions ................................................................................................. 66
Chapter 1 Review Exercises ...................................................................................................................... 76
Extended Application: Using Extrapolation to Predict Life Expectancy ................................................... 88
CHAPTER 2 EXPONENTIAL, LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS
2.1 Exponential Functions ..................................................................................................................... 89
2.2 Logarithmic Functions .................................................................................................................... 99
2.3 Applications: Growth and Decay ...................................................................................................109
2.4 Trigonometric Functions ................................................................................................................114
Chapter 2 Review Exercises .....................................................................................................................122
Extended Application: Power Functions ..................................................................................................133
CHAPTER 3 THE DERIVATIVE
3.1 Limits .............................................................................................................................................134
3.2 Continuity .......................................................................................................................................145
3.3 Rates of Change .............................................................................................................................152
3.4 Definition of the Derivative............................................................................................................163
3.5 Graphical Differentiation ................................................................................................................178
Chapter 3 Review Exercises .....................................................................................................................182
Extended Application: A Model for Drugs Administered Intravenously .................................................194
, CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives .............................................................................................. 196
4.2 Derivatives of Products and Quotients .......................................................................................... 205
4.3 The Chain Rule.............................................................................................................................. 212
4.4 Derivatives of Exponential Functions ........................................................................................... 221
4.5 Derivatives of Logarithmic Functions ........................................................................................... 239
4.6 Derivatives of Trigonometric Functions........................................................................................ 248
Chapter 4 Review Exercises .................................................................................................................... 253
Extended Application: Managing Renewable Resources ........................................................................ 263
CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................ 265
5.2 Relative Extrema ........................................................................................................................... 278
5.3 Higher Derivatives, Concavity, and the Second Derivative Test................................................... 293
5.4 Curve Sketching ............................................................................................................................ 316
Chapter 5 Review Exercises .................................................................................................................... 336
Extended Application: A Drug Concentration Model for Orally Administered Medications.................. 360
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................... 361
6.2 Applications of Extrema ................................................................................................................ 370
6.3 Implicit Differentiation .................................................................................................................. 383
6.4 Related Rates................................................................................................................................. 399
6.5 Differentials: Linear Approximation ............................................................................................. 406
Chapter 6 Review Exercises .................................................................................................................... 410
Extended Application: A Total Cost Model for a Training Program ....................................................... 421
CHAPTER 7 INTEGRATION
7.1 Antiderivatives .............................................................................................................................. 423
7.2 Substitution.................................................................................................................................... 429
7.3 Area and the Definite Integral ....................................................................................................... 437
7.4 The Fundamental Theorem of Calculus ........................................................................................ 451
7.5 The Area Between Two Curves .................................................................................................... 465
Chapter 7 Review Exercises .................................................................................................................... 480
Extended Application: Estimating Depletion Dates for Minerals ............................................................ 493
CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION
8.1 Numerical Integration.................................................................................................................... 494
8.2 Integration by Parts........................................................................................................................ 508
8.3 Volume and Average Value .......................................................................................................... 517
8.4 Improper Integrals ......................................................................................................................... 525
Chapter 8 Review Exercises .................................................................................................................... 533
Extended Application: Flow Systems ...................................................................................................... 545
SOLUTIONS MANUAL
BEVERLY FUSFIELD
CALCULUS
FOR THE LIFE SCIENCES
SECOND EDITION
Raymond N. Greenwell
Hofstra University
Nathan P. Ritchey
Edinboro University
Margaret L. Lial
American River College
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
,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.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2015 Pearson Education, Inc.
Publishing as Pearson, 75 Arlington Street, Boston, MA 02116.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written
permission of the publisher. Printed in the United States of America.
ISBN-13: 978-0-321-96448-9
ISBN-10: 0-321-96448-9
www.pearsonhighered.com
,CONTENTS
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials ....................................................................................................................................... 1
R.2 Factoring............................................................................................................................................ 3
R.3 Rational Expressions ......................................................................................................................... 4
R.4 Equations ........................................................................................................................................... 7
R.5 Inequalities. ..................................................................................................................................... 11
R.6 Exponents ........................................................................................................................................ 21
R.7 Radicals ........................................................................................................................................... 24
CHAPTER 1 FUNCTIONS
1.1 Lines and Linear Functions ............................................................................................................. 28
1.2 The Least Squares Line ................................................................................................................... 39
1.3 Properties of Functions .................................................................................................................... 46
1.4 Quadratic Functions; Translation and Reflection ............................................................................ 54
1.5 Polynomial and Rational Functions ................................................................................................. 66
Chapter 1 Review Exercises ...................................................................................................................... 76
Extended Application: Using Extrapolation to Predict Life Expectancy ................................................... 88
CHAPTER 2 EXPONENTIAL, LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS
2.1 Exponential Functions ..................................................................................................................... 89
2.2 Logarithmic Functions .................................................................................................................... 99
2.3 Applications: Growth and Decay ...................................................................................................109
2.4 Trigonometric Functions ................................................................................................................114
Chapter 2 Review Exercises .....................................................................................................................122
Extended Application: Power Functions ..................................................................................................133
CHAPTER 3 THE DERIVATIVE
3.1 Limits .............................................................................................................................................134
3.2 Continuity .......................................................................................................................................145
3.3 Rates of Change .............................................................................................................................152
3.4 Definition of the Derivative............................................................................................................163
3.5 Graphical Differentiation ................................................................................................................178
Chapter 3 Review Exercises .....................................................................................................................182
Extended Application: A Model for Drugs Administered Intravenously .................................................194
, CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives .............................................................................................. 196
4.2 Derivatives of Products and Quotients .......................................................................................... 205
4.3 The Chain Rule.............................................................................................................................. 212
4.4 Derivatives of Exponential Functions ........................................................................................... 221
4.5 Derivatives of Logarithmic Functions ........................................................................................... 239
4.6 Derivatives of Trigonometric Functions........................................................................................ 248
Chapter 4 Review Exercises .................................................................................................................... 253
Extended Application: Managing Renewable Resources ........................................................................ 263
CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................ 265
5.2 Relative Extrema ........................................................................................................................... 278
5.3 Higher Derivatives, Concavity, and the Second Derivative Test................................................... 293
5.4 Curve Sketching ............................................................................................................................ 316
Chapter 5 Review Exercises .................................................................................................................... 336
Extended Application: A Drug Concentration Model for Orally Administered Medications.................. 360
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................... 361
6.2 Applications of Extrema ................................................................................................................ 370
6.3 Implicit Differentiation .................................................................................................................. 383
6.4 Related Rates................................................................................................................................. 399
6.5 Differentials: Linear Approximation ............................................................................................. 406
Chapter 6 Review Exercises .................................................................................................................... 410
Extended Application: A Total Cost Model for a Training Program ....................................................... 421
CHAPTER 7 INTEGRATION
7.1 Antiderivatives .............................................................................................................................. 423
7.2 Substitution.................................................................................................................................... 429
7.3 Area and the Definite Integral ....................................................................................................... 437
7.4 The Fundamental Theorem of Calculus ........................................................................................ 451
7.5 The Area Between Two Curves .................................................................................................... 465
Chapter 7 Review Exercises .................................................................................................................... 480
Extended Application: Estimating Depletion Dates for Minerals ............................................................ 493
CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION
8.1 Numerical Integration.................................................................................................................... 494
8.2 Integration by Parts........................................................................................................................ 508
8.3 Volume and Average Value .......................................................................................................... 517
8.4 Improper Integrals ......................................................................................................................... 525
Chapter 8 Review Exercises .................................................................................................................... 533
Extended Application: Flow Systems ...................................................................................................... 545
