I am trying to grasp the concept of Taylor remainder.
Online lecture taught me that in equation
$R_n^{(n+1)}(x) = f^{(n+1)}(x) + T_n^{(n+1)}(x)$,
$T_n^{(n+1)}(x)$ becomes zero because in general nth polynomial when taken derivative n+1 times becomes zero. For example, $x^2$ when taken derivatives 3 times it becomes zero, 2x, 2, then 0.
So the lecture goes $R_n^{(n+1)}(x) = f^{(n+1)}(x)$.
But I am not getting it because why not $R_n^{(n+1)}$ and $f^{(n+1)}$ also do not become zero?
I don't quite get the idea of nth derivative of f function becoming error itself, though I am not sure if my interpretation is even right.