教学中,有学生问及函数凹凸性判定定理在多元函数中的形式,根据一元函数有关理论,存在以下一般结论. 定理:若f(X)在Rn中的开凸集D上存在二阶连续偏导,则(?)X∈D,f(X)是凹(凸)函数的充要条件为:f(X)的海塞方阵 In teaching, some students ask about the form of the function assumption of convexity in a multivariate function. According to the one-variable function theory, the following general conclusions exist. Theorem: If f(X) exists in the open convex set D in Rn For partial derivatives, the necessary and sufficient condition for (?)X∈D,f(X) to be a concave (convex) function is: f(X) of the Hesse square