I've solved hundreds of these kind of problems and then I came across this one. Well, normally, I'd say that it cannot be solved in closed form, only to realise that it is given to first year undergraduate students. So I must be overseeing something

Find extremal points of f(x,y):

$\displaystyle f(x,y)=x^2 + y^2 + 2x + 4y - 8 \sqrt{x y} + 4$