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…