MATH 210 Study Guide - Final Guide: Talking Lifestyle 1278, Partial Derivative, Fxx
Document Summary
Problem 1 solution: find and classify the critical points of the function f (x, y) = x3 + 3xy y3. The partial derivatives of f (x, y) = x3 + 3xy y3 are fx = 3x2 + 3y and fy = 3x 3y2. 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 = 3x2 + 3y = 0 fy = 3x 3y2 = 0 y = x2. Substituting this into equation (2) and solving for x we get: (1) (2) (3) We observe that the above equation is satis ed if either x = 0 or x3 1 = 0 x = 1. Nd the corresponding y-values using equation (3): y = x2: if x = 0, then y = 02 = 0, if x = 1, then y = (1)2 = 1.
