I'm tutoring a student who is in a typical precalculus/trig course where they're teaching her about graphing various arbitrary polynomials. Among the rules of multiplicity and intercepts they seem to be phrasing the questions such that they expect the students to also find the maxima and minima of the polynomial as well. How do they expect their students to do this without calculus or the aid of a calculator? I was embarrassed sitting there with her mother not sure if I should teach the girl how to differentiate or not to answer the problem. But their the problem was, explicitly asking for the maxima of the function and saying no calculators allowed. I'm stumped, is there anyone who knows what they're looking for?