对“关于曲线拐点判别法”一文中某些问题的探讨

THE THEORETICAL ANALYSIS OF SOME ERROR REASONS FOR THE PAPER"ON THE METHODS OF JUDGING OF INFLECTION"

文[1]中给出了判别曲线上点是否为拐点的两个充分条件。然而两个定理的证明却是错误的。本文通过具体的反例阐述了其证明错误的原因,并且同时否定了其中的一个定理的推论,进而给出另外一定理的正确证明。

In the paper[ 1 ] Two-sefficieney methods of Judging point of inflection are given. But the proof of two theorems have mistakes. In this paper, we analyse the error reasons through the counter example, point out that the corollary of one theorem is uncorrect under some circumstance. And also give a correct proof of another theorem.