Problem 1. (10 points) Using the method of Lagrange multipliers, find the points on the sphere x2 + y2 + 22 = 25 that maximize and minimize the function f (x, y, z) = x + 2y + 3z. Problem 2. (10 points) Find the Taylor polynomial up to degree 2 terms (i.e., the quadratic approximation) about the point x = 1, y = 1 to the function f(x, y) = In(3x + 2y - 4) - 1