Nelson advanced functions & introductory calculus

696 Pages·2002·39.484 MB·English

by  Chris Kirkpatrick, Rob McLeish, Ralph Montesanto, Christine Suurtamm, Susanne Trew, David Zimmer

Advanced Functions&
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NELSON
Advanced Functions &
Introductory Calculus
Authors
Chris Kirkpatrick
Rob McLeish
Ralph Montesanto
Christine Suurtamm
Susanne Trew
David Zimmer
THOMSON
NELSON
THOMSON
Se ae
NELSON
Advanced Functions & Introductory Calculus,
Chris Kirkpatrick, Ralph Montesanto,
Susanne Trew, Christine Suurtamm,
Robert McLeish, David Zimmer
Director of Publishing Senior Designer Creative Art/Technical Art
David Steele Suzanne Peden Irma Ikonen, David McKay,
Deborah Crowle, Steven Corrigan,
Publisher, Mathematics Creative Director Marie Price, Peter Papayanakis
Cheryl Turner Angela Cluer
Printer
Program Manager Production Coordinator Transcontinental Printing Inc.
Colin Garnham Sharon Latta Paterson
The authors thank the following
Project Manager Cover Design for their assistance in the
- Robert Templeton, Peter Papayanakis development of this book: David
First Folio Resource Group, Inc. Wright; Andrew Dmytriw;
Composition
Susan Smith; Jan and Barry Scully;
Senior Production Editor Nelson Gonzalez
Vanessa Davison; First Folio
Linh Vu
Photographs and Permissions Resource Group Inc.: Matthew
Content Editors Maria DeCambra Calder, Susan Cartier, Katrina Koh,
Don Rowsell, Mike Waters Jane Lee, Alan Leung, Khai Quoc
Performance Task Authors Ngo, and Linda Nigro.
Copy Editor Mary Bourassa, Donna Del Re,
Susan Marshall Don Rowsell, Susan Smith
COPYRIGHT © 2002 by Nelson, a ALL RIGHTS RESERVED. No part of National Library of Canada
division of Thomson Canada this work covered by the copyright Cataloguing in
Limited. hereon may be reproduced, Publication Data
transcribed, or used in any form or
Printed and bound in Canada
by any means-graphic, electronic, Main entry under title:
i) 22 8} ZY Ey) Yl ORY or mechanical, including Nelson advanced functions and
For more information contact photocopying, recording, taping, introductory calculus
Nelson, 1120 Birchmount Road, Web distribution or information Includes index.
Scarborough, Ontario, M1K 5G4. storage and retrieval ISBN 0-17-615778-6
Or you can visit our Internet site at systems—without the permission of
http://www.nelson.com. the publisher. 1. Functions. 2. Calculus. |.
For permission to use material Kirkpatrick, Chris.
from this text or product, contact QA37.2.N44 2002 515
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Advisory Panel
Kaye Appleby Beverly Farahani Irene McEvoy
Retired Kingston CVI Coordinator,
(formerly Thames Valley DSB) Limestone DSB Peel DSB
Dan Charbonneau Robert Fleischauer Jack Weiner
St. Charles College Centre Wellington DHS, Department of Mathematics
Sudbury Catholic DSB Upper Grand DSB University of Guelph
Richard Clausi Shawn Godin Kathy Wilkinson
Elmira DSS, Cairine Wilson SS Collingwood Cl,
Waterloo DSB Ottawa-Carleton DSB Simcoe County DSB
Angela Con Mary Howe
St. Elizabeth CES Coordinator,
Peterborough Victoria London Catholic DSB
Northumberland Clarington
Catholic DSB
Reviewers
lan Anderson Mary Ellen Diamond Reno Palombi
Ancaster HS, Consultant, Consultant,
Hamilton-Wentworth DSB Niagara RCSB Algoma DSB
Arlene Angel-Blair Frank Di Pietro Sue Pyke
John McCrae SS Consultant, Richview Cl,
Ottawa-Carleton DSB Windsor-Essex CDSB Toronto DSB
John Battaglia Domenic Greto John Santarelli
Catholic Central HS, Brother Andre CHS, Cathedral HS,
Windsor-Essex CDSB York CDSB Hamilton-Wentworth CDSB
Alex Belloni John Katic Tom Santowski
Mother Teresa CHS, Woodroffe High School Rothwell Osnabruck School
Ottawa-Carleton CSSB Ottawa-Carleton DSB Upper Canada DSB
Mary Bourassa Pat Kehoe Alex Shum .
Lisgar Collegiate Mother Teresa CHS, Royal St. George’s College
Ottawa-Carleton DSB Ottawa-Carleton CSSB Toronto
Louise Brighton Clara Madonia
Peter Wei
Mother Teresa CHS, Don Bosco HS,
Toronto CDSB Toronto CDSB North Toronto Cl
Toronto DSB
Karen Bryan Frank Maggio
Betsy Wimbs
North Dundas DHS, Consultant,
Toronto DSB
Upper Canada DSB Halton CDSB
Ernmond Wong
Mike Cafferata Tom May
Thornlea SS
Agincourt Cl, Opeongo HS
York Region DSB
Toronto DSB Renfrew County DSB
Bill Woodcock
Marcia Charest Elizabeth Pattison
Meadowvale SS Westlane SS, Consultant,
Peel DSB Niagara DSB Lambton-Kent DSB
Contents
Introduction
Part 1
Advanced Functions
Chapter 1
Polynomial Function Models 1
The Chapter Problem 8)
Chapter Challenges 4
Getting Ready oh
1.1 Polynomial Functions 6
1.2 Investigating the Characteristics of Polynomial Functions 19
1.3 Creating New Polynomial Functions: An Introduction to Composition 28
1.4 Dividing Polynomials 39
1.5 Factoring Polynomials 4S
1.6 Solving Polynomial Equations 54
1.7 Solving Polynomial Inequalities 65
Chapter | Review ies
Chapter 1 Performance Task 79
Chapter | Review Test 80
Chapter 2
Exponential and Logarithmic Function Models 81
The Chapter Problem 82
Chapter Challenges 83
Getting Ready 84
2.1 Investigating Exponential Models 86
2.2 Graphs of Exponential Functions 96
2.3 Various Forms of Exponential Functions 107
2.4 The Logarithmic Function 114
2.5 Laws of Logarithms eal
2.6 Solving Exponential Equations 128
2.7 Creating Logarithmic Models 135
2.8 Solving Logarithmic Equations 143
2.9 Creating and Applying Exponential and Logarithmic Models 149
Chapter 2 Review 157
Chapter 2 Performance Task 163
Chapter 2 Review Test 164
Cumulative Review Test 1 165
Part 2
Differential Calculus: Polynomial and
Rational Functions :
Chapter 3
Rates of Change in Polynomial Funcdan Models 167
The Chapter Problem 168
Chapter Challenges 169
Getting Ready 170
3.1 Examining Rates of Change in Polynomial Models 172
3.2 A Closer Look at Rates of Change: The Tangent Problem 183
3.3 Limits of Polynomial Functions 194
3.4 Using Limits to Find Instantaneous Rates of Change — ;
The Derivative 206
3.5 Finding Some Shortcuts — The Constant and Power Rules 2
. 3.6 Finding Some Shortcuts — The Sum and Difference Rules 225
3.7 Polynomial Function Models and the First Derivative 2353
3.8 Polynomial Function Models and the Second Derivative 247
Chapter 3 Review ZG
Chapter 3 Performance Task 261
Chapter 3 Review Test 262
Chapter 4
Using the Derivative to Analyze Polynomial
Function Models 263
The Chapter Problem 264
Chapter Challenges 265
Getting Ready 266
4.1 Analyzing a Polynomial Function: Intervals of Increase
and Decrease 268
4.2 Maximum and Minimum Values of a Polynomial Function 200
4.3 The First Derivative Test 286
4.4 Finding Some Shortcuts — The Product Rule 296
4.5 Finding Optimal Values for Polynomial Function Models 303
4.6 Rates of Change in Business and Economics 313
4.7 Sketching Graphs of Polynomial Functions: Concavity 322
Chapter 4 Review 334
Chapter 4 Performance Task 339
Chapter 4 Review Test 340
vi CONTENTS