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When deriving the five-point differentiation formula as shown in this book, the IVT was used to combine $ f^{(5)} (\xi_1) $ and $ f^{(5)} (\xi_2) $ into one error term, $ f^{(5)}(\tilde{\xi}) $

As the book says here, another method is used to combine $ f^{(5)}(\tilde{\xi}) $ and $ f^{(5)}(\hat{\xi}) $.

What is the method used here?

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    What's the relation between $\xi_1$, $\xi_2$, $\tilde{\xi}$ and $\hat{\xi}$?2012-12-10

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