I am looking for a function of on an interval with several local optima that appears in some mathematical model and which you can at least imagine that you want to optimize.
I am teaching a calculus course right now, and as usual there is a short chapter on optimization. I wanted to have give a list of examples of functions on an interval $[a,b]$ that you might want to optimize and which display different behavior.
Now I find it easy to give examples of monotone functions from applications and it is also not difficult to find good examples of applied problems where the functions you optimize is U-shaped.
But I actually got stuck trying to find good examples of more complex behavior with several local optima with an applied motivation.
Ideally the function I am looking for should come from a real application in science or otherwise and you should at least be able to imagine that you want to optimize it. It has to be a single-variable function and it would be better the less knowledge one needs to understand what the function is modelling.