We give the proof of Taylor's theorem as promised at the end of the last class.
This completes the proof.
We apply Taylor's theorem to $F(t)$.
We examine the implications on $f(x,y)$.
We observe some consecuences pointing to min/max properties of $f(x,y)$.
If you are interested you can find a different presentation of these arguments in number theory books. The key term to search for is "binary forms".