We can calculate the maximum error of a Taylor-polynomial of n order with the following formula:
$$ R_n(x)=\frac{f^{(n+1)}(\xi)(x-c)^{(n+1)}}{(n+1)!}, $$
I know how to use this formula but I'm trying to understand more how everything works under the hood.
More specifically, why can we use the next n+1 term of a n-Taylor polynomial with a derivative value of $\xi$ to get the maximum error?