Calculus Animations,Graphics and Lecture Notes

Optimization for Functions of 2 Variables

About Kelly Liakos
Calculus 1- Limits and Derivatives
Calculus 1 - The Second Derivative
Calculus 1 and 3 Formula Sheets
Chain Rule
Computer Lab Assignments
Conic Sections
Differential Equations
Directional Derivatives/Gradient
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1st order Diff Eqs -Motion
Flux Integrals and Surface Integrals
Infinite Sequences
Infinie Series
Level Curves and Level Surfaces
Line Integrals
Optimization and Related Rates
Optimization for Functions of 2 Variables
Parametric Equations 2-space
Parametric Equations 3-space
Partial Derivatives
Polar Coordinate System
Polar Coordinates- Derivatives and Integrals
Riemann Sums and the Fundamental Theorem of Calculus
2d order Diff EQS-Motion
2d Partial Derivatives
Supplemental Exercises and Solutions
Tangent Planes/ Differential for f(x,y)
Trigonometry Applications
Triple Integrals
Unit Tangent Vectors/Unit Normal Vectors
Vectors in General
Vector Valued Functions
Visualizing Limits of Functions of 2 Variables
Special Topics
Scratch Paper
2 Poems

The discssion of optimization is broken into 5 lectures:
1.locating local extrema
2.classifying local extrema using contour diagrams and gradient fields
3.classifying local extrema using the second partials test extrema
5.Lagrange Multipliers

Locating Local Extrema

Classifying Local Extrema using Contour Diagrams and Gradient Fields

Classifying Local Extrema with the 2d Partials Test

Global Extrema

Global Extrema - LaGrange's Theorem

The following 2 questions are concerned with the optimization of functions of 2 variables

1. Find and classify all local extrema of f(x,y) = x2 + 2y2 -x2y

2. Let f(x,y = xy - x - y +3  on the triangular region with vertices (0,0),(2,0), and (0,4)

Find the global extrema.

Solutions to Optimization Problems

The Smart Bunny-A very short story by Kurt Vonnegut Jr.

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