由条件,f(0)＝lim f(x)＝lim f(x)/x * lim x=1*0＝0.
且f'(0)＝lim （f(x)－f(0))/x=lim f(x)/x＝1.
以上极限都是x趋于0.
因为f''(x)>0,故f‘(x)是严格递增的,故f'(x)>f'(0)＝1,
令g(x)＝f(x)－x,g'(x)＝f'(x)－1>0,当x>0时,
g(x)是递增的,故g(x)>g(0)＝f(0)－0＝0,于是得
f(x)>x,当x>0时.