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Optimization for Functions of 2 Variables

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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
4.global 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



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