Taylor's Theorem/One Variable/Statement of Theorem/Also presented as

Taylor's Theorem in One Variable Also presented as
Taylor's Theorem in One Variable can also be presented in a form like this or similar:

Let $f$ be a real function which is at least $n + 1$ times differentiable on the open interval $\openint a b$.

Let $\xi$ be a real number in $\openint a b$.

Then for a given $x \in \openint a b$:

where $E_n$ satisfies:
 * $E_n = \dfrac 1 {\paren {n + 1}!} \paren {x - \xi}^{n + 1} \map {f^{\paren {n + 1} } } \eta$

for some $\eta$ between $x$ and $\xi$.