Consider the function f(x, y) = x 3 y 3 + 81xy .

a) Find the critical points of f.

b) Suppose we are optimising f . Would it make sense at this point to check the sufficiency conditions?

c) Use the second order test to categorise each critical point(s) as a local minimum, local maximum, saddle point, or inconclusive. Suppose the domain is now restricted to 0 x 3 and 0 y 10.

d) Sketch/graph the domain. e) (3 points) Find the point that maximises f on this domain