L24 Math 233 Lecture Notes - Lecture 23: Lagrange Multiplier, Nissan L Engine, Linear Independence
L24 Math 233 verified notes
23/45View all
Document Summary
Find critical points i. e. find where the gradient vector = 0. Check the values of f and the second derivatives f f xx yy f xy. For maximum and minimum in a domain less than the entirety of two dimensions. Find the critical points i. e. find where the gradient vector = 0. Parameterize boundaries to get equations and check those too x. + 2 = 1 x (x, ) y = y = x2 + y2. Method 1: parameterize the constrained surface (the constraint) For example, x = x, so x) y = 2 (1. For h"(x) to equal 0, x = 3/13. Looking at the equation g(x,y), x and y can be arbitrarily large as long as they have different signs. Thus, plugging these large values of x and y into f, f(x,y) can be infinitely large- there will be no maximum. That means the point at x = 3/13 is a minimum.
