Let f R²->R be defined by

f(x, y) = (ay)/(x² + y² + 2) where a ≠ 0

1. Show that there exist two stationary points, and show that their coordi- nates are independent of a.
2. Show that one stationary point will always be a maximum and the other always a minimum.
3. a = 1 and consider the level curve
f(x, y) = 1/10 .

Identify the set of points on this curve, where there exists a function, g, such that y = g(x) .