2. (14 points) Maximization on Descartes' Folium. Consider the maximization problem max s.t. z + 33 = 9zy I!y (note, the objective function in simply f(z,y) = ). If by any chance your answer - - - - - 3 contains roots without rational answers, just leave them as is (e.g. \\/i), do not compute a numerical approximation. a) (6 points) Find the stationary points, using the Lagrange multiplier method. b) (4 points) The bonus question on the midterm exam was \"Find all the points on the Folium of Descartes where an implicit function = f(z) does not exist.\" Explain why the stationary points (z,y) you have found in a) are the same as the answer to this bonus question. @(4 points) For one of the stationary points (only one to save you time, you're welcome), say whether it is a local maximum, a local minimum, or whether you can't tell using the principal minor tests seen in class. Note: You can do it for more than one point, but only the first point will be graded