The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My question is very short, and very simple. Is there a name for the $c$ guaranteed by the Mean Value Theorem? If I had to name it now, I would call it the mean value abscissa?
Many of these classical theorems were proved before the current language of calculus. This means it is possible, perhaps even likely, that such a $c$ was originally given a name.