1. Find the local maxima of the function:
(1) f(x,y) = xy, subject to the constraint that
x+y-1=0. Result should be 1/4.
2. Find the local minima of the functions:
(1) f(x,y) = x^2+y^2, subject to the constraint that
xy-3=0. Result should be 6.
(2) f(x,y) = x^2+4xy+y^2, subject to the constraint
that x-y-6=0. Result should be -18.