9. (11 pts) Find all the critical points of f(x,y) = x^3 + 3y^2 - 6xy + 3 and classify them as local minimums, local maximums, or saddle points.
10. (11 pts)
(a) Find the maximum and minimum values of f(x,y) = x^2 + y^2 - 2y + 7 subject to the constraint x^2 + y^2 = 4.
(b) The function also has a critical point at (0, 1). Find the global minimum of f(x,y) on the set D = {(x,y) | x^2 + y^2 ≤ 4}
11. (8 pts) Below is the contour map of g(x,y). Use it to answer the following. Briefly explain or show your work.
(a) Estimate g_y(0, 1).
(b) Is the directional derivative of g at (0, -1) in the < 1, 1 > direction positive, negative, or zero?
(c) Is ∇g(2,0) parallel to i, -i, j, or -j?