Given $f \in C^{n+1}[a, b]$, let the $n$ th-degree polynomial $p$ interpolate the values $f\left(x_{i}\right)$, $i=0,1, \ldots, n$, where $x_{0}, x_{1}, \ldots, x_{n} \in[a, b]$ are distinct. Given $x \in[a, b]$, find the error $f(x)-p(x)$ in terms of a derivative of $f$.