Theorem 12

Let [Maple Math] be a function for which all derivatives of order [Maple Math] or less are continuous over [Maple Math] . Let [Maple Math] be [Maple Math] distinct numbers in [Maple Math] . Then there exists a number [Maple Math] in ( [Maple Math] ) with [Maple Math] .


This means that if the underlying function is smooth, the higher order divided differences become very small and the interpolating polynomial can be truncated at some point.