关于“以曲代曲证明不等式”的思考与探究

• 作 者: 黄建锋
• 机 构: 浙江省余姚市第二中学,
• 出 处: 数学通讯
• 发表日期: 2015年08期
• 关键词: 不等式证明 构造函数 单变量 轮换对称 切线法 证法 偏导 恒成立 线控制 当且仅当

所谓的“独立和型”对称不等式,是说存在一个单变量函数f(t)使得不等式可以写成如下形式:∑ni=1f(xi)≤C(≥C),C为常数.f(x)对于满足条件v=A(≥A,≤A)或∏ni=1=1x=1,证明“独立和型”对称不等式,文[1],[2],[3]等提出“以曲代曲”证明不等式的思想:构造函数y=f(x)在均值x=An处的曲线y=g(x)=λ(xn-An)

The so-called “independent and type” symmetric inequality means that there exists a univariate function f (t) such that the inequality can be written as follows: Σni = 1f (xi) ≤C (≥C) and C is constant .f x) Prove that “independent and type ” symmetric inequalities, such as [1], [2], [3] and so forth, satisfy the condition of v = A (≥A, ≤A) or Πni = 1 = 1x = The idea of ​​proving inequality: The curve of the constructor y = f (x) at the mean x = An y = g (x) = λ (xn-An)