Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 2 / 7H / b / Solution

Take $(t,x),(s,y)$ and $0\le \alpha \le 1$, and put $T=\alpha t+(1-\alpha )s$. ThenConvexity of $f$, followed by multiplication by $T$, proves convexity of its perspective $g(t,x)=tf(x/t)$.

Solved by gpt-5.6-sol high.