Mean value theorem (divided differences)
From Wikipedia, the free encyclopedia
The mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. It states that for given n + 1 points of an n-times differentiable function f there exists an interior point where the nth derivative of f equals n! times n-th divided difference at these points.
![\exists \xi\in[\min\{x_0,\dots,x_n\},\max\{x_0,\dots,x_n\}] \ f[x_0,\dots,x_n] = \frac{f^{(n)}(\xi)}{n!}](../../../../math/a/c/0/ac06d7b591ab85bcb98812c6ee8dd5f8.png)
[edit] Special cases
For n = 1, that is two function points, you obtain the simple mean value theorem.
[edit] Applications
The theorem can be used to generalise the Stolarsky mean to more than two variables.
