Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 5 / d / Solution

Substituting $y=-x$ cancels both the cubic and linear terms, leaving $f(x,-x)=0$ for every real $x$. Thus the constrained maximum and minimum are both zero, attained everywhere on the constraint line. The feasible set is unbounded, but the restricted function is constant; compactness is not needed here.