Example 2. Construct a table of divided differences of various orders for the following values of $x$ and $y=f(x)$:

\[
\begin{gathered}
x_{0}=-3, x_{1}=-2, x_{2}=-1, x_{3}=1, x_{4}=2 \\
y_{0}=-9, y_{1}=-16, y_{2}=-3, y_{3}=11, y_{4}=36
\end{gathered}
\]