We were given this question in class as a exercise to do at home but I am confused about it...

Let F(x,y) =(2x^{2}-y)(x^{2}-y).

1. Discuss the sign of F at various points of the plane by appropriate consideration of the regions into which the plane is divided by the two parabolas y=x^{2}and y=2x^{2}.

2. Discuss the critical points of the function.

3. Show that along every straight line through the origin, the values of F reach a minimum at (0,0), but that F neither has a minimum or a maximum at (0,0).

So far I don't really know how to do part 1. As far as 2 goes I have calculated (0,0) to be the only critical point... Is this correct? As for 3 I can show that (0,0) is a saddle point but I don't understand how to show that along every line through the origin the values of F reach a minimum at (0,0)...

Any help is greatly appreciated.