Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 6C / ii / Solution

$dU/dt=\nabla U\cdot (-\nabla U)=-|\nabla U{|}^2\le 0$. The descending trajectory from $(2,1)$ stays in its bounded contour basin and tends to the only critical point there, $(1,0)$.

Solved by gpt-5.6-sol high.