This graph has been scaled by the factor \(-\beta=e^6-2\). The function \(p(Z_{si})\) has been ignored, although the following table can be obtained,
\(\begin{matrix} x& f^{'}(x) \\ x=1& -2 \\x=2 &+1 \\x=3 &-2 \end{matrix}\)
The graphs does not end at x=4, but approaches zero as x approaches infinity; the integral graph approaches -1.
The following plot is when \(E_s=0\) is also a root.
In this case \(\beta=-1\). Similarly, the graphs approaches zero as x approaches infinity and the integral approaches -1.
Have a nice day.
