All three are possible.
The table tells us that for certain x and y, we have f(x) < f(y) if x < y. There's also no evidence that f(x) = f(y) for some points x ≠ y in the interval, so f(x) could easily be monontonically increasing. (I is true)
If we assume f(x) is strictly increasing (which does not contradict the given table) on the entire interval, we have f'(x) > 0. A positive function can be strictly increasing. (II is true)
A function is concave up on an interval if its derivative is increasing on that interval. This follows from statement (II) if it happens to be true. (III is true)
(E)