Lagrange polynomial extrapolation errors

Question

Lagrange polynomial interpolation error term is: $$E(x)=\frac{f^{(n+1)}(ζ)}{(n+1)!}π_{n+1}(x)$$ where $π(x)=(x−x_0)…(x−x_n)$ and $ζ∈(a,b)$.
However, the theorem doesnot include the situation when $x \notin [a,b]$.
My question is when considering $x \notin [a,b]$, is the error term still the same? If not, please tell me what is the formula for extrapolation errors. Thanks a lot!