JEE Main 2005 Mathematics question on Limits Continuity and Differentiability

1. A.
   $f''(x) = 2$, $\forall \ x \in (R)$
2. B.
   $f''(x) = f'(x)$, for some $x \in (1, 3)$
3. C.
   there exists atleast one $x \in (1, 3)$ such that $f''(x) = 2$
4. D.
   None of the above

[AIEEE 2005]