The code:

At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\[
   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]
where $h$ is some step.
Then we interpolate points $\{(x_k,f_k)\}$ by polynomial
\begin{equation} \label{eq:poly}
   P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
   \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}
Here are references to existing equations: (??), (??).
Here is reference to non-existing equation (??).

The output:

Note that the output is an image, because of a basic incompatibility between the the WP QuickLaTeX and Enlighter plugins. (Basically, the WP QuickLaTeX plugin will attempt to render LaTeX code anywhere on the page, regardless of where the [latexpagecode] shortcode occurs, even if it’s located in a highlighted syntax block. It would be nice if it only attempted to render code that follows the shortcode, but that is not a feature at the present time.