Multiple discriminants and extreme values of polynomials of several variables

An extreme value of a function is the value of the function at one of its extremum points. Each extremum point of a differentiable function of several variables is described by the system of equations expressing the vanishing of all partial derivatives. However, in the general case, one cannot obtain equations for extreme values of the function. The case of polynomials significantly differs from the general case, and in this paper we obtain an equation for extreme values of a given polynomial of several variables.