\begin{equation*}
f''(x) = e^{x}(x^{2} + x - 13)
\end{equation*}
Using these provided derivatives, find all critical numbers of the original function \(f(x)\text{,}\) and then use the first or second derivative tests to classify them as local maximums, local minimums, or neither. Then give the intervals on which \(f\) is increasing or decreasing.
