question_answer

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

A)  \[f''(x)<0\]for all x

B)  \[-1<f''(x)<0\]for all x

C)  \[-2\,\underline{<}\,\,f''(x)\,\,\underline{<}-1\]for all x

D)  \[f''(x)<-2\] for all x

E)  None of these