Question

当x趋向于0时,limf(x)/x=1,且f‘’(x)>0,证明：f(x)>=x

Answer 1

由limf(x)/x=1知f(0)=0且f '(0) = 1.

令g(x)=f(x)-x

有g(0)=0

g ' (x) = f ' (x) - 1

g' (0) = 0

g'' (x) = f ''(x)>0

所以 g(x)>=0,证毕