f(x)=x^2-2mx+2m+1在x属于[0,1]时恒大于0,求m的取值范围

问题描述:

f(x)=x^2-2mx+2m+1在x属于[0,1]时恒大于0,求m的取值范围

f(x)=x^2-2mx+2m+1
=(x-m)^2-(m-1)^2+2 >0
(x-m)^2>=0>(m-1)^2-2
-(m-1)^2+2>0
1-√2