# 10.4 | The Error in Taylor Polynomial Approximations

Suppose $$f$$ and all its derivatives are continuous. If $$P_n(x)$$ is the $$n^{th}$$ Taylor polynomial for $$f(x)$$ about $$a$$, then
$$|E_n(x)| = |f(x) – P_n(x)| \leq \frac{M}{(n+1)!}|x-a|^{n+1},$$
where $$|f^{n+1}(x)| \leq M$$ on the interval between $$a$$ and $$x$$.