what about something like this?
This one was a little tricky actually, but again, let's use some intuition (you'd want something a little more rigorous in an exam).
The particle starts going to the right at 4ms^-1. The acceleration is negative after x=1, and this will eventually turn it around. When it returns to x=1 it is travelling backwards:
The acceleration is zero at this point, and although between x=0 and x=1 it will be positive acceleration, it won't be enough to turn it back around, the thing is going to zoom off to negative infinity. This can also be gleamed from the fact that the expression for velocity only has a single root at about x=2.5, the point where it turned around initially. Besides that, it ain't stopping, so it does return to the origin and then zooms off to negative infinity