a statement that claims that given an arc of a differentiable curve, there is at least one point on that arc at which the derivative of the curve is equal to the average derivative of the arc
In mathematics, two theorems, one associated with differential calculus and one with integral calculus. The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line connecting the endpoints of the function's graph on that interval. For example, if a car covers a mile from a dead stop in one minute, it must have been traveling exactly a mile a minute at some point along that mile. In integral calculus, the mean value of a function on an interval is, in essence, the arithmetic mean (see mean, median and mode) of its values over the interval. Because the number of values is infinite, a true arithmetic mean is not possible. The theorem shows how to find the mean value using a definite integral. See also Rolle's theorem