At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\(f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\)
=================
$x^2-x-9=0$
==== do thi – bbt —
$$
f(x) = \frac{1}{x^2 + x}
\begin{tikzpicture}
\draw[->] (-1,0) — (3,0) node[right] {$x$};
\draw[->] (0,-1) — (0,2) node[above] {$f(x)$};
\draw[domain=0.2:2.5,smooth,variable=\x,blue] plot ({\x},{1/(\x*\x + \x)});
\end{tikzpicture}
$$