What are the values and types of the critical points, if any, of #f(x,y)=y^2-x^2+3x-sqrt(2xy-4x)#?
A saddle point at
The stationary points are found solving
Whose real solution(s) is
The qualification is made calculating the Hessian matrix in this point.
with characteristic polynomial
The roots are non null with oposite signs so the stationary point found, is a saddle point.