设函数f(x)在x=0的某邻域内可导,f'(0)=0,limf'(x)/sinx=-1/2问f(0)是f(x)的极大值还是极小值?

Question

设函数f(x)在x=0的某邻域内可导,f'(0)=0,limf'(x)/sinx=-1/2问f(0)是f(x)的极大值还是极小值?

Answer 1

构造f(x)=-x^2/4 满足条件0 极大值或用罗必塔法则 处理极限式 可知二阶导数小于0