Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 6 / a

Under the hypotheses of Taylor's theorem with Lagrange remainder, for example $f\in C^{n+1}$ on an interval containing $x$ and $x+h$, there is a point $\xi$ between them such thatThe Lagrange remainder makes this an exact equality, rather than just a truncated Taylor polynomial. For $h=0$ the equality is immediate.