question_answer

There exists a function \[f(x)\]satisfying \[f(0)=1\], \[f'(0)=-1,\ f(x)>0\]for all x and                    [Kurukshetra CEE 1998]

A)            \[f(x)<0\],\[\forall x\]

B)            \[-1<f''(x)<0,\,\forall x\]

C)            \[-2<f''(x)\le -1,\,\forall x\]

D)            \[f''(x)<-2,\,\forall x\]