1. Find all critical point(s) of the function f given by f(x, y) = xy2-3x - 2x- y. Classify each as the location of a saddle point, relative maximum, or relative minimum. [7/2 marks] = 2. Suppose that g(x,y) x+4y - 4 and f(x, y) = 3xy. Consider the point P on the ellipse with equation g(x, y) = 0 at which f(x, y) is largest. Show that the slope of the tangent line to the level curve g(x, y) = 0 at P is 3. [3/2 marks] There are different possible approaches to the second problem: you can apply the method of Lagrange multipliers to find the point and calculate the slope of the tangent line, or you can approach the problem more theoretically to see why the slope is 3 without as much calculation. Carrying out either approach correctly earns all of the points.