player1_1_1 said:sorry, I didnt explain it good:) i need to know how can I classify stationary to extreme points or non-ekstreme depending on hessian?
The Hessian matrix is a square matrix of second-order partial derivatives of a function of two variables. It is commonly used in multivariate calculus to determine the critical points of a function and classify them as maxima, minima, or saddle points.
The determinant of the Hessian matrix being 0 indicates that the function has a critical point, but it does not provide information about the nature of that critical point. This can lead to ambiguity in determining the optimal solution to a problem.
Yes, it is possible for a function to have a Hessian matrix of 0 at a non-critical point, but this is not a common occurrence. In most cases, a Hessian matrix of 0 indicates a critical point.
The second derivative test states that if the second partial derivatives of a function are continuous and the Hessian matrix is positive definite at a critical point, then that critical point is a local minimum. Similarly, if the Hessian matrix is negative definite, the critical point is a local maximum. If the Hessian matrix is indefinite, the critical point is a saddle point.
Yes, the Hessian matrix is always a square matrix since it is composed of second-order partial derivatives, which are taken with respect to two variables. The size of the matrix is determined by the number of variables in the function.