Find the extremum of $f(x,y)$ subject to the given constraint, and state whether it is a maximum or a minimum.
$f(x,y) = x^2 + 2y^2 - 4xy$; $x + y = 21$
Find the Lagrange function $F(x,y,\lambda)$.
$F(x,y,\lambda) = \boxed{}$ - $\lambda$ $\boxed{}$
Find the partial derivatives $F_x$, $F_y$, and $F_\lambda$.
$F_x = \boxed{}$
$F_y = \boxed{}$
$F_\lambda = \boxed{}$
There is a $\boxed{}$ value of $\boxed{}$ located at $(x, y) = \boxed{}$.
(Type an integer or a fraction. Type an ordered pair, using integers or fractions.)
