Find he local maximum and minimum value and saddle points of the function: $$f(x,y)=x^2-xy+y^2-9x+6y+10$$
The answer is a min of $(-4,1), f(-4,1)=73$
I got a min of $(12/5,-21/5)$ my $$ f_x=2x-y-9\\ f_y=-x+2y+6 $$ set $f_x = 0 = f_y$ and we get $x=(9+y)/2$ so $y=-21/5$ and $x=12/5$
I found out that this was a minimum by the 2nd derivative test. There are no max or saddle points.