CAJ | 학술논문

同济大学《高等数学》最值理论中有结论称“若一个函数在一个区间内可导且只有一个驻点，并且这个驻点是函数的极值点，那么此驻点也是该函数的最值点”，但并未给出证明。学生们对此频感好奇。受Fermat引理启发，利用反证法可获一个比此结论更为一般的定理。
동제대학《고등수학》최치이론중유결론칭“약일개함수재일개구간내가도차지유일개주점，병차저개주점시함수적겁치점，나요차주점야시해함수적최치점”，단병미급출증명。학생문대차빈감호기。수Fermat인리계발，이용반증법가획일개비차결론경위일반적정리。
“If a differentiable function on an interval has only one stationary point ,and the stationary point is a local extremum point of the function ,then the stationary point is also the global extremum point of the function”is a statement appeared ,without proof ,in the textbook of Higher Mathematics published by Tongji university . Students are usually curious about how to prove the result .In this paper ,inspired by Fermat’s lemma ,we establish a theorem ,which is more general than the result above .