(2) Consider $f(x,y) = xy$ on the ellipse $x^2 + 2y^2 = 1$.
(a) Find the maximum of $f(x, y)$ on the ellipse
(b) Find the points on the ellipse $x^2 + 2y^2 = 1$ where $f(x,y) = xy$ obtains its
maximum
(c) Find the minimum of $f(x, y)$ on the ellipse
(d) Find the points on the ellipse $x^2 + 2y^2 = 1$ where $f(x, y) = xy$ obtains its
minimum.