I am asked to find all local extreme values & saddle points of
$f(x,y) = 2x^2 + y^2 - xy - 7y + 8$
$f_x(x, y) = 4x-y, \qquad f_y(x,y) = 2y-x-7$
$f_x(x,y) = 0, \qquad y = 4x$
$f_y(x,y) = 0, \qquad 2y-x-7 = 0, \qquad x = 1$
So I have a critical point at $(1,4)$. Then I use 2nd derivative test to check min/max
$f_{xx}(x,y) = 4, \qquad f_{yy}(x,y) = 2, \qquad f_{xy}(x,y) = -1$
$H(x,y) = 4\times 2 + (-1)^2 = 9$
$H(1,4) > 0$, $f_{xx} > 0$ so local min. Answer given is "Local min $-6$ at $(1,4)$". What does $-6$ refer to?