On Jul 10, 2013, at 4:40 PM, Joe Niederberger <email@example.com> wrote:
> That the mean value theorem is a highly *visually* intuitive fact,
To whom Joe? I have seen NO class of students get anything like the MVT from a picture, UNLESS it is explained to them. Connectedness (a term I will use for what you feel for that curve) is an intuitive rat-sense fact. Connectedness is NOT the MVT. I am not saying that you cannot reason and reflect about connectedness, and maybe even come up with the MVT, but that is not the rat-sense you are talking about. That requires all of the elements of reasoning that any other domain does.