Chapter 2 Differentiation. Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Figure 2.1: Tangent Line to a Graph.

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Presentation transcript:

Chapter 2 Differentiation

Copyright © Houghton Mifflin Company. All rights reserved.2 | 2 Figure 2.1: Tangent Line to a Graph

Copyright © Houghton Mifflin Company. All rights reserved.2 | 3 Figure 2.2: Tangent Line to a Graph at a Point

Copyright © Houghton Mifflin Company. All rights reserved.2 | 4 Figure 2.3: Tangent Line to a Circle

Copyright © Houghton Mifflin Company. All rights reserved.2 | 5 Figure 2.6: The Secant Line Through the Two Points

Copyright © Houghton Mifflin Company. All rights reserved.2 | 6 Figure 2.7: Secant line approaches the tangent line

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 Definition of the Derivative

Copyright © Houghton Mifflin Company. All rights reserved.2 | 9 Figure 2.11: Functions That Are Not Differentiable at x = 0

Copyright © Houghton Mifflin Company. All rights reserved.2 | 10 Differentiability Implies Continuity

Copyright © Houghton Mifflin Company. All rights reserved.2 | 11 Figure 2.12: The Constant Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 12 Figure 2.13: The (Simple) Power Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 13 The Constant Multiple Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 14 The Sum and Difference Rules

Copyright © Houghton Mifflin Company. All rights reserved.2 | 15 Figure 2.18: Definition of Average Rate of Change

Copyright © Houghton Mifflin Company. All rights reserved.2 | 16 Definition of Instantaneous Rate of Change

Copyright © Houghton Mifflin Company. All rights reserved.2 | 17 Marginal Profit/Marginal Revenue/Marginal Cost

Copyright © Houghton Mifflin Company. All rights reserved.2 | 18 Figure 2.22: Discrete and Continuous Variables

Copyright © Houghton Mifflin Company. All rights reserved.2 | 19 The Product Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 20 The Quotient Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 21 Figure 2.28: The Chain Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 22 The General Power Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 23 Summary of Differentiation Rule

Copyright © Houghton Mifflin Company. All rights reserved.2 | 24 Notation for Higher-Order Derivatives

Copyright © Houghton Mifflin Company. All rights reserved.2 | 25 Position Function/Velocity Function/Acceleration Function

Copyright © Houghton Mifflin Company. All rights reserved.2 | 26 Implicit Differentiation

Copyright © Houghton Mifflin Company. All rights reserved.2 | 27 Guidelines for Solving a Related-Rate Problem

Copyright © Houghton Mifflin Company. All rights reserved.2 | 28 Table: Verbal Statement/ Mathematical Model

Copyright © Houghton Mifflin Company. All rights reserved.2 | 29 Simplifying Algebraic Expressions