1. (a) Consider the function f(33,y) = 232 + 921 2y +1, where a: = tcos(9), y = tsin(9). Calculate % at the point (13,6) = (2,7r). (4 marks) (b) Consider the function g(x,y) = 3:2 2x + 4y4 +1. (i) Find the gradient of g at the point (:1:,y) = (2, 1). (ii) Find a unit vector u such that Dug(2, 1) = 0. (iii) Find the equation of the tangent line to the level curve of g at the point (2,1). (7 marks) (c) Consider the function ay) = (x 1)2 +92 +33%! $- Find one critical point of f and classify it using the second derivative test. (5 marks) ((1) Suppose we want to nd the point on the parabola y = :62 whose distance to the point (:c, y) = (3, 4) is a minimum. Use the method of Lagrange multipliers to derive a system of equations (in x, y, A) that we would use to solve this problem. (You do NOT need to solve the equations.) (4 marks)