     Calculus Animations,Graphics and Lecture Notes Optimization for Functions of 2 Variables    Home About Kelly Liakos Sponsors 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 Double Integrals Equillibrium Solutions 1st order DEs 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 PreCalculus 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 Trigonometry Applications Triple Integrals Unit Tangent Vectors/Unit Normal Vectors Vectors in General Vector Valued Functions Visualizing Limits of Functions of 2 Variables Work Links 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
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 variables1. Find and classify all local extrema of f(x,y) = x2 + 2y2 -x2y2. 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.  