Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 2F / a / Solution

LetBy the regular level set theorem, $F^{-1}(0)$ is a smooth surface wherever $\nabla F\ne 0$. A critical point on the level set would satisfyThese equations imply $4a^3+27b^2=0$. Therefore

Solved by gpt-5.6-sol high.