# What are the values and types of the critical points, if any, of #f(x,y)=y^2-x^2+3x-sqrt(2xy-4x)#?

##### 1 Answer

A saddle point at

#### Explanation:

Given

The stationary points are found solving

or

Whose real solution(s) is

The qualification is made calculating the Hessian matrix in this point.

so

with characteristic polynomial

with roots

The roots are non null with oposite signs so the stationary point found, is a saddle point.