MATH237 Study Guide - Quiz Guide: Lagrange Multiplier, Apple Juice

Consider the function

f(x, y) = x² + xy + y²

defined on the unit disc, namely,

D = {(x, y)| x² + y² ? 1}.

Use the method of Lagrange multipliers to locate the maximum and minimum points for f on the unit circle. Use this to determine the absolute maximum and minimum values for f on D.