In the sufficient condition of the extremum of binary function, when AC-B ^ 2 > 0, will there be a > 0, C0, which is the minimum value, a or C

In the sufficient condition of the extremum of binary function, when AC-B ^ 2 > 0, will there be a > 0, C0, which is the minimum value, a or C

AC one positive one negative, AC

How to judge the maximum and minimum of multivariate function extremum

1. If there are no restrictions, take the binary function as an example, the first step is to find the point when the first partial derivatives of the function are all zero, and record it as point P0, where point P0 is a stable point, and then verify the positive definiteness of the heesen matrix. If it is positive definite, the minimum value is obtained at point P0; if it is negative definite, the maximum value is obtained at point P0; if it is indefinite, the extreme value is not obtained
(specific judgment formula)
2. If there are restrictive conditions, for example, the restrictive condition is ψ (x, y) = 0, then there are two methods
1. Dimension elevation: construct Lagrange function, use Lagrange multiplier method as a necessary condition to solve, and then verify whether the extreme value is obtained
2. Dimension reduction: there are many ways to solve this problem, such as using parameterization or u (x, y, z) = 0, if the restriction condition is ψ (x, y, z) = 0, then an expression about Z will be obtained: Z (x, y) = 0, which will be brought into U (x, y, z). In this way, the original function will be reduced from 3 dimensions to 2 dimensions, which is more convenient

How to judge the maximum and minimum of a function?

Find the second order reciprocal