Question

Lim(X趋向于0)f(X)/X=1,f''(X)>0证明f(X)大于等于X

Answer 1

设g(x) = f(x) - x ,g'(x) =f'(x) -1,g"(x)=f("x) 当g'(x) =0,f'(x) =1 => x=0 因 limx=>0[f(X)-f(0)]/(X-0)=1 ,g(x) =0g"(x)=f("x)>0 g'(x) 单调递增 所以 x=0 是 g'(x)=0 的唯一解g(x) = f(x)-x >=0