In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are approximated using a graphing calculator. In this article, the authors show that it is possible to find the relative maximum and minimum values of a cubic polynomial by using elementary techniques that are appropriate for any algebra or precalculus course. (Contains 5 figures.)