Check if the function below is concave.
$$f(x,y) = (x-2)(2000+4\sqrt y-20x) - 10000 - y$$
I tried finding the eigenvalue for the Hessian where
$$det(H-\lambda) = det \begin{pmatrix} -40-\lambda & \frac{2}{\sqrt y} \\ \frac{2}{\sqrt y} & -\frac{x-2}{y^{3/2}} - \lambda \end{pmatrix} = 0 $$ but I got stuck because the eigenvalue is dependent on x and y.
Is there another way to do this, aside from using the definition of concavity?