Question

请用Taylor公式证明设limx趋近0 f(x)/x=1 且f"(x)>0,证明f(x)>=x

Answer 1

首先f(O）=[limx趋近0 x]*[limx趋近0 f(x)/x]=0*1=0;

其次f'(0)=limx趋近0 [f(x)-f(0)]/(x-0)=limx趋近0 f(x)/x=1.

则f(x)=f(0)+f'(0)x+f''(a)x^2/2>=f(0)+f'(0)x=x.