Question

From lecture 27: Positive Definite Matrices and Minima In one of the examples,
A = 2 6
6 20
So, x'Ax = 2x^2 + 12xy + 20y^2

Supposedly, there is a minima when
2x^2 + 12xy + 20y^2 > 0
and this is supposed to be equivalent to A being positive definite.

However, when I take the 2nd derivative matrix of the function 2x^2 + 12xy + 20y^2, I get
fxx fxy
fyx fyy
=
4 12
12 40
instead of
2 6
6 20

Why is this so?