I need to maximize this function on the positive real line:
$$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be around $x=514$, but I could not use mathematica to show it. My plot has a peak at $x=680$ instead. I want to ask if anyone has any idea how to get the correct answer.
The code I am using now is:
A = 1/Gamma[x]^{14}*(301.6/(14*x))^{-14 *x}*(1.22578*10^{19})^{x -1} E^{-14 x}
and I plot it by
Plot[A, {x, 513, 700}, PlotPoints -> 1000]
The result is something very strange:
NMaximize
I'm getting results depending on the upper bound ofx
. However withNMaximize[{f[x], 10^3 > x > 0}, x]
I get{1.82059*10^-9, {x -> 514.197}}
which seems correct comparing with an appropriate plot. $\endgroup$