# Taylor Polynomial Exploration, Part 1

$T_n(x)$ is the $n^{th}$ Taylor Polynomial of $f(x)$ 1) Drag the point $x_0$ along the $x$-axis to change the center of expansion. 2) Slide $n$ to change the degree. 3) Enter a new function in the text box to change the function.

[b]Taylor's Theorem[/b]: There exists $\xi$ between $x$ and $x_0$ such that $f(x)-T_n(x)=R_n(x)$ where $R_n(x)=\frac{f^{n+1}(\xi)}{(n+1)!}(x-x_0)^{n+1}$