Critical point classification

Find and classify the critical points of

Hey guys let me know if you got something similar or something different
so I got the derivative of f(x,y)=4x^2 - 2xy + y^2 - x - 2y.

df/dx = 8x-2y-1
df/dy = 2y-2x-2
I proceeded to add the functions together and got
6x-3=0 Y cancels out
6x=3 Add three on both sides
x=1/2
So I plugged this in and for the function 2y-2x-2 set that =0
then its 2y-2(1/2)-2=0
2y=3
y=3/2
So my critical point is (1/2,3/2)
dxx =8
dxy=-2
dyy=2
8*2-(-2^2) = 16-4 so that means I have a minimum at 12

@fcarrill Looks like you’ve got a great start! You just need to finish the classification.