It should be possible to find the minima/maxima of a model, e.g. polynomial fit or other model (I would assume).
Tom Richards most recently suggested the importace of this, e.g. for eclipsing variables. As he said in email to me: "The first thing every eclipsing binary person wants is to find the minimum of a light curve (or, for RR Lyrae and the like, maxima). I couldn’t find a way of doing this. (If V* knows the polynomial equation, it just has to find where the differential = 0.)"