The mean value theorem states that if a function is differentiable in an open interval

and continuous in its closure

, then there exists a point

such that

. This theorem's semi-discrete analog suggests that if a function is tendable in

, continuous in

, and also that

, then for each

there exists a point

, such that

, where

is the function's tendency, and "tendability of a function" means that the tendency operator can be applied to the function. The definition of the tendency operator is given in the Demonstration "Detachment and Tendency of a Single Variable Function". A comparison between the mean value theorem and its semi-discrete analog is found in the details. When compared to the original theorem, this version depicts a trade-off between the functions for which the theorem's correctness holds and the kind of information that the theorem gives. This version is called semi-discrete due to the decisive role of the

function, whose image is finite. In this Demonstration, you can vary the parameters

,

, and

from the theorem's statement to better understand the theorem. The highlighted yellow points

are those whose existence is assured by the theorem.