关于函数凸性点的两个结论

Two Conclusions about the Convex Point of a Function

本文证明了（ａ，ｂ）内连续可导函数ｆ（ｘ）的每个点都是凸性点与ｆ（ｘ）是凸函数互为充要条件；拉格朗日中值定理的逆定理在函数的凸性点是成立的．

This paper demonstrates that every point of a continuous derivable function f(x) within (a, b) is a convex point, f(X) is a convex function, and they are mutual conditions. Thus, the converse theorem of lagrange's mid - value theorem is established at theconvex point of the function.