Goal: Use the Method of Lagrange Multipliers to find the maximum and minimum values of the function f(x, y, z) subject to the constraint that (x, y, z) lie on the sphere a2 + y? + z2 = 1. = - x + 2y – 2z We denote the constraint function as g(x, y, z) = x² + y? + z? – 1. (1) The gradients of the objective function f and the constraint function g are given by: V f(x, y, z) = ( V g(x, y, z) = ). (2) The maximum for f occurs at (x, y, z) = ( ), and the maximum value of f is (3) The minimum for f occurs at (x, y, z) = ( ), and the minimum value of f is

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