Chapter 2
Differentiation
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2
Tangent Line to a Graph
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 3
Tangent Line to a Circle
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 4
Tangent Lineto a Graph at a Point
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 5
The SecantLine Through the Two Points
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 6
Secant lineapproaches the tangent line
TheTangentLineProblem.cdf
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 7
Definition of the Slope of a Graph
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 8
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 9
Definition of the Derivative
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 10
Functions ThatAre Not Differentiable at x = 0
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 11
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 12
The Constant Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 13
The (Simple)Power Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 14
The Constant Multiple Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 15
The Sum and Difference Rules
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 16
Definition ofAverage Rate of Change
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 17
Definition ofInstantaneous Rate of Change
TheDefinitionOfTheDerivative.cdf
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 18
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 19
The Product Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 20
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 21
The Quotient Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 22
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 23
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 24
The Chain Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 25
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 26
The General Power Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 27
Summary of Differentiation Rule
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 28
Marginal Profit/Marginal Revenue/Marginal Cost
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 29
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 30
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 31
Notation forHigher-Order Derivatives
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 32
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 33
Position Function/Velocity Function/Acceleration Function
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 34
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 35
Implicit Differentiation
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 36
Table: Verbal Statement/Mathematical Model
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 37
Guidelines for Solvinga Related-Rate Problem
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 38
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 39
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 40
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 41
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 42
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 43
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 44
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 45
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 46
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 47
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 48
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 49
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 50
RelationOfRadiusSurfaceAreaAndVolumeOfASphere.cdf
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 51
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 52
Copyright © Houghton Mifflin Company. All rights reserved. 2 | 53
Find the slope of the graph at the given point.