I have the following formula which represents the cost $s$ of an action on a particular day:
$s = (c\sum\limits_{n=1}^l n)^{d/l}$
I want to choose $l$, so that $s$ is minimised, given a particular $c$ and $d$.
Notes
* I will want to do the action many times per day.
* On any particular day, $d$ is given, but it may be different on different days.
* $c$ is also given, but may be different each time I do the action.
* For $l$, I can choose any integer between $1$ and $d$ (inclusive).
* $d$ will be an integer. Realistic values are around $100$ to $10000$, although higher and lower are possible. It will always be at least $1$, if that matters.
* $c$ will be a positive number (greater than $0$).
How do I determine the value for $l$ that results in the lowest possible $s$, given $c$ and $d$?