MATH 210 Study Guide - Final Guide: Saddle Point, Maxima And Minima, Cross Product
Document Summary
Problem 1 solution: let f (x, y) = 1 maximum, local minimum, or saddle point. Find all critical points of f (x, y) and classify each as a local. The partial derivatives of f (x, y) = 1. 3 x3 + y2 xy are fx = x2 y and fy = 2y x. These derivatives exist for all (x, y) in r2. Thus, the critical points of f are the solutions to the system of equations: Solving equation (1) for y we get: fx = x2 y = 0 fy = 2y x = 0 y = x2. Substituting this into equation (2) and solving for x we get: (1) (2) (3) 2(cid:0)x2(cid:1) x = 0 x(2x 1) = 0. We nd the corresponding y-values using equation (3): y = x2: if x = 0, then y = 02 = 0, if x = 1. Thus, the critical points are (0, 0) and ( 1.
