It was first stated by another French mathematician, Joseph-Louis Lagrange.
This theorem states that: If a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b),
then there exists at least one number 'c' in (a, b) such that
Geometrical interpretation of the mean value theorem: Geometrically, the theorem says that somewhere between points A and B on a differentiable curve, there is at least one tangent line parallel to secant line AB.
Physical interpretation of the mean value theorem: If we think of as the average rate of change of the function f over the interval [a, b]
and (c) as an instantaneous rate of change,
then the mean value theorem says that there must be a point in the open interval (a, b) at which the instantaneous rate of change is equal to the average rate of change over the interval [a, b].