Originally Posted by

**marianne** I've found the following statement in my textbook:

If $\displaystyle f: I \subset \mathbb{R} \rightarrow \mathbb{R}$ is a function of class $\displaystyle C^2$, than there exists $\displaystyle \varepsilon \in <0, 1>$ such that $\displaystyle f(x+h)=f(x) + h f'(x) + \frac{h^2}{2} f'' (x+\varepsilon h)$

This is not a consequence of anything we've done in the lesson, so I was hoping someone could tell me is what this expansion is.

Thank you!

(It reminds me of Taylor series, but it's not, I think..)