设函数f(x)=√3sin∏x/m.若存在f(x)的极值点x″满足x″²+[f(x)]²<m²,则m的取值范围是?

问题描述:

设函数f(x)=√3sin∏x/m.若存在f(x)的极值点x″满足x″²+[f(x)]²<m²,则m的取值范围是?

πx'/m=(k+1/2)π,k∈Z,
∴x'=m(k+1/2),
由题设得[m(k+1/2)]^2+[√3sin(πx/m)]^20,
∴k=0,-1,①变为[√3sin(πx/m)]^22或m