设g(x)=f(x)-x
依题意,limf(x)/x=1
∴ f(0)=limf(x)=lim[f(x)/x·x]=limf(x)/x·limx=0
f '(0)=limf(x)/x=1
∴ g(0)=0,g'(0)=f '(0)-1=0
又 g''(x)=f ''(x)>0
所以,g(0)=0是g(x)的极小值,也是最小值.
于是,g(x)≥0恒成立,
∴ f(x)≥x
超级试练试题库
© 2017-2019 超级试练试题库,All Rights Reserved.