函数极值的必要条件是众所周知的,然而,无论是高中数学教材还是一般的工科高等数学教材,对函数极值的充分条件均没有讲解透彻,在掌握了第二充分条件f′(x0)=0且f″(x0)≠0后,自然会想到,对于f′(x0)=0且f″(x0)=0的情况又该如何,这个问题导致许多高中学生和高校学生对此类问题 However, no matter whether it is a high school mathematics textbook or a general engineering math textbook, the sufficient conditions for the extremum of the function are not thoroughly explained. After we have mastered the second sufficient condition f ’(x0) = 0 and f “(x0) ≠ 0, it is of course self-evident that this problem has led many high school and college students to think of such problems as f ’(x0) = 0 and f” (x0) = 0