Lesson 6.3: Maximum/minimum Problems

In this lesson, you will study optimization problems.

View all of the instructional videos, read the provided readings, and practice exercises/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided.

Lesson Objectives

Upon completion of the lesson 6.3, you will be able to:

• Analyze and determine extrema

• Model and solve applications

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. Determining the Relative Extrema of a Function of Two Variables [8:53]

   1. Source: bullcleo1 from YouTube

1. Absolute Extrema of Functions of Two Variables [9:18]

   1. Source: bullcleo1 from YouTube

1. Second Derivative Test (find and classify the critical points of the function) [8:39]

   1. Source: MIT from YouTube

1. Max/Min | MIT 18.02SC Multivariable Calculus, Fall 2010 [13:59]

   1. Source: MIT from YouTube

1. Applications of Extrema of Functions of Two Variables I [9:49]

   1. Source: bullcleo1 from YouTube

1. Applications of Extrema of Functions of Two Variable III [8:59]

   1. Source: bullcleo1 from YouTube

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. Relative Minimums and Maximums

2. Paul’s Online Math Notes

3. Absolute Minimums and Maximums

4. Paul’s Online Math Notes

   1. Lecture 18 – Extrema

   2. by Eitan Angel

5. Second Derivative Test

6. WolframMathWorld

7. Locating and Classifying Local Extrema

8. SD. Second Derivative Test

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

1. Maxima and Minima for Functions of Two Variables

2. S. F. Ellermeyer

3. Max/Min for Functions of Two Variables

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Two Variable Local Extrema Examples

2. Section 14.8 Maxima & Minima of Functions of Two Variables

Homework Assignment

Do Homework 6.3 on MyMathLab.

Show Your Work Assignment

Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.

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