It appears that you are correct.
The correct answer cannot be the first, sixth, seventh, or eighth graphs. The reason for this is that when there is a horizontal asymptote, by definition the $y$ component of the graph is unchanging. In other words, if you zoom in very closely, you can see that at that point that a tangent line to that point will have a slope of $0$. Thus $f'(c) = 0$, not $f'(c) < 0$.
The forth graph might not even be defined at $c$, but if it is defined it falls under the previous category.
Lastly the third and fifth graphs cannot be the answer as the $y$ component is increasing as $x$ increases. Thus the tangent line to the point would have a positive slope, so $f'(c) > 0$, not $f'(c) < 0$.
Thus the only possible solution is the second graph.