@SarGe I think that your answer is a good intuitive explanation of what's going on here, but that's not what the OP is after: they're looking for a proof. If you were to alter your post so that it contained a proof (perhaps hidden behind spoiler text, which one can make by starting a line with >! ) I think it would be received better.
Saying something like "Hint: look at this graph. What do you notice? Full details of a solution under the spoiler text below" would be in line with how I've tried to approach such problems when I'm trying to give a hint as an answer.
There's also the matter that sometimes a hint is not really appropriate as an answer - it can sometimes be hard to tell when this is the case, but sometimes one really does need to throw the asker a life-preserver and rescue them from their confusions. I'm not saying this is the case in your specific post (indeed, I don't hang out much in the calculus tag and I haven't taught the subject for a while), but I would like to point out it's sometimes appropriate.
