MATH 210 Study Guide - Final Guide: Spherical Coordinate System, Cylindrical Coordinate System, Talking Lifestyle 1278
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Problem 1 solution: let f (x, y) = 3x2 + xy + 2y2. Find the partial derivatives f best linear approximation of f at (1, 1) and use it to estimate f (1. 1, 1. 2). Y , at (1, 1), and nd the. Solution: the linearization of f (x, y) = 3x2 + xy + 2y2 about (1, 1) has the form: L(x, y) = f (1, 1) + fx(1, 1)(x 1) + fy(1, 1)(y 1) The rst partial derivatives of f (x, y) are: The value of f (1. 1, 1. 2) is estimated to be the value of l(1. 1, 1. 2): L(x, y) = 6 + 7(x 1) + 5(y 1) f (1. 1, 1. 2) l(1. 1, 1. 2) f (1. 1, 1. 2) 6 + 7(1. 1 1) + 5(1. 2 1) f (1. 1, 1. 2) 7. 7. Problem 2 solution: find and classify the critical points of the function f (x, y) = x3 3xy + y3.
