论常量函数的充分必要条件

The Judgment of Constant Function

常量函数是最简单的函数,判定满足某些条件的函数是否为常量函数并不简单.由拉格朗日中值定理容易得出:"在区间I上f(x)为常量函数的充分必要条件是对任意的x∈I都有f′(x)=0".在此基础上进一步给出并证明了函数为常量函数的另外几个充分必要条件,在理论上为证明"满足某些条件的函数是常量函数"提供了切实可行的证明方法.

Constant function is the simplest function,but its judgment is not simple.It is clear to see from Lagrange theorem ＂The enough and essential condition of f（x） being constant function is f′（x）=0＂.Several enough and essential conditions of being constant function are given to prove it.It also supply practical ways to prove that ＂function meeting certain requirements is constant function＂.