Mean value theorem (divided differences)

In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. == Statement of the theorem == For any n + 1 pairwise distinct points x0, ..., xn in the domain of an n-times differentiable function f there exists an interior point ξ ∈ ( min { x 0 , … , x n } , max { x 0 , … , x n } ) {\displaystyle \xi \in (\min\{x_{0},\dots ,x_{n}\},\max\{x_{0},\dots ,x_{n}\})\,} where the nth derivative of f equals n!

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