In Problems 1 through 6 let A = E" for the indicated n.
1. Find the critical points, relative extrema, and saddle points. Make a sketch indicating the level sets.
(a) f(x, y) = x - x² - y².
(c) f(x, y) = sin(xy).
(b) f(x, y) = (x + 1)(y-2).
(d) f(x, y) = xy(x − 1).
(c) Maximum at each point where xy = n/2 + 2m; minimum at each point where xy = -π/2 + 2mn, m any integer. Saddle point at 0