Brain fart on my part, try f(x)=x^3, f'(x)=3x^2, f''(x)=6x, so the difference quotient at x=0 is h^3>0 for h>0, but the first two derivatives are zero.
(the problem arrose because of a last minute replacement of a much more interesting counter example, the point was that you can construct a function satisfying the required condition but which satisfy none of the given candidates for the answer, as an alternative consider f(x)=x^4)
In fact the conditions on f'' cannot apply even if assorted ">"s are changed to ">="'s because there is no condition requiring f'' to exist.
Now there may be a formulation of a question like this that does have an answer like c, but this is not that question.
RonL