A function value and a derivative

A fictional mathematics exercise defines f(x) = x cubed minus three x squared plus five for every real x. It asks separately for f(2) and the derivative evaluated at two. A learner differentiates correctly but gives the derivative value as the original function value, then says a zero derivative always proves a global minimum. The problem supplies no restricted interval or request for a global optimization proof. Students must keep evaluation and rate of change distinct, calculate both requested quantities and explain why an additional conclusion needs its own reasoning. The example concerns a polynomial, so there is no hidden denominator or logarithm domain restriction to invent.