连续可微函数的一个性质

A Property of Continuous and Differentiable Function

对于连续可微函数,依据Rolle定理,可以证明在其两个相邻稳定点之间是严格单调的.下面作为定理的应用并给出了一个反例,以此说明了一元函数极值的第一判定定理是一个充分条件而非必要条件.

The paper proves that the continuous and differentiable function is strictly nonoscillatory between two adjacent stable points with the ROUe theorem, and that an opposite example is given as application of the theorem. This example shows that the first theorem to extremum of function is a sufficient condition but a needful condition.