The Hessian

The Hessian, which is also known as discriminant or Hessian matrix, was introduced in the year 1844 by Hesse, German mathematician, born in 1811 and dead in 1874. This Happened after that, Carl Gustav Jacob Jacobi introduce "The Jacobian".

The Hessian to determine the maximum and minimum of a function of two variables, also this one in optimization:

     - If the Hessian is positive, it is a minimum or maximum, depending on whether the second derivative of x is negative will be a maximum positive or if there is a minimum.

     

 -If the Hessian is negative, there will be a saddle point where there will be both maximum and minimum out of the same point.

     

 -If the Hessian is zero, we have enough information to determine anything, unless we see the full function drawn.