Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 2G / iii / Solution

Statement (iii) is false. On the unit disc, takeThe function $f$ is continuous on the closed disc, but $\varphi$ has its strict maximum $1$ at the interior point $(0,0)$ and equals zero on the boundary.

Solved by gpt-5.6-sol high.