Extrapolation of graphs is always invalid. And as Feynman pointed out you're usually better off ignoring the last point on the graph as well - if the last point was any good they'd have been able to make further measurements, so the last point is probably lousy.
So, if we ignore the last point, that makes the second-to-last point the real last point, and we start again. Eventually we have no graph
Out of interest, do you have a reference to your Feynman 'quote'? Thanks. I once started to plough through his 'Lectures in Physics'. Probably do so again sometime in the future. Never read anything else but I believe that he's quite a good novelist.