Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.4 Modeling and Optimization.

Slides:



Advertisements
Similar presentations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Related Rates Section 4.6.
Advertisements

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.4 Rates of Change and Tangent Lines.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.6 Related Rates.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Modeling and Optimization Section 4.4.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.6 Related Rates.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Extreme Values of Functions Section 4.1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Exponential and Logarithmic Functions Section 3.9.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chain Rule Section 3.6.
4.4 Modeling and Optimization What you’ll learn about Examples from Mathematics Examples from Business and Industry Examples from Economics Modeling.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.4 Fundamental Theorem of Calculus.
AP CALCULUS AB Chapter 4: Applications of Derivatives Section 4.4:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.3 Connecting f ’ and f ” with the graph of f.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Antiderivatives and Slope Fields Section 6.1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Linearization and Newton’s Method Section 4.5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.2 L’Hôpital’s Rule.
Copyright © 2011 Pearson, Inc. 7.5 Systems of Inequalities in Two Variables.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Fundamental Theorem of Calculus Section 5.4.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.1 Sequences.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 3.9 Derivatives of Exponential and Logarithmic Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Rules for Differentiation Section 3.3.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Quadratic Equations.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.4 Lengths of Curves.
Calculus Vocabulary 4.4 Modeling and Optimization Strategy for Solving Max-Min Problems 1.Understand the Problem: Read the problem carefully. Identify.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.3 Antidifferentiation by Parts.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Product and Quotient Rules for Differentiation.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 8.4 Improper Integrals.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Trigonometric Functions Section 3.5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 9.5 Testing Convergence at Endpoints.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.5 Logistic Growth.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Chapter 5 Integration.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 11.6 Calculus of Vector-Valued Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Mean Value Theorem Section 4.2.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.5 Trapezoidal Rule.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.3 Complex Numbers Quadratic Equations in the Complex Number System.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Integral As Net Change Section 7.1.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.4 Logarithmic Functions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Integration by Substitution Section 6.2.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 1 Quick Review.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.1 Integral As Net Change.
The Inverse Trigonometric Functions (Continued)
Sinusoidal Curve Fitting
Section 9.1 Polar Coordinates
Section R.8 nth Roots; Rational Exponents
Building Exponential, Logarithmic, and Logistic Models from Data
Section 2.4 Circles Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Equations Quadratic in Form Absolute Value Equations
Section 8.3 The Law of Cosines
Section 11.8 Linear Programming
Equations Quadratic in Form Absolute Value Equations
Copyright © 2008 Pearson Prentice Hall Inc.
Copyright © 2008 Pearson Prentice Hall Inc.
Section 2.2 The Graph of a Function
Modeling and Optimization
Section 2.2 The Graph of a Function
Mathematical Models: Building Functions
Copyright © 2008 Pearson Prentice Hall Inc.
Copyright © 2008 Pearson Prentice Hall Inc.
Partial Fraction Decomposition
Section 3.2 The Graph of a Function
Sinusoidal Curve Fitting
Quadratic Equations in the Complex Number System
Partial Fraction Decomposition
Properties of Rational Functions
Copyright © 2008 Pearson Prentice Hall Inc.
Copyright © 2008 Pearson Prentice Hall Inc.
The Inverse Trigonometric Functions (Continued)
Presentation transcript:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.4 Modeling and Optimization

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 2 Quick Review

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 3 Quick Review Solutions

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 4 What you’ll learn about Examples from Mathematics Examples from Business and Industry Examples from Economics Modeling Discrete Phenomena with Differentiable Functions …and why Historically, optimization problems were among the earliest applications of what we now call differential calculus.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 5 Strategy for Solving Max-Min Problems

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 6 Example Inscribing Rectangles

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 7 Maximum Profit

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 Example Maximizing Profit

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 9 Minimizing Average Cost