In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives.
[1] For any n + 1 pairwise distinct points x0, ..., xn in the domain of an n-times differentiable function f there exists an interior point where the nth derivative of f equals n !
times the nth divided difference at these points: For n = 1, that is two function points, one obtains the simple mean value theorem.
be the Lagrange interpolation polynomial for f at x0, ..., xn.
Then it follows from the Newton form of
that the highest order term of
be the remainder of the interpolation, defined by
zeros: x0, ..., xn.
By applying Rolle's theorem first to
ξ
This means that The theorem can be used to generalise the Stolarsky mean to more than two variables.