Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 12E / d / Solution

No. Take the constant function $f(t)=c>0$, which has $f\prime =0$. The claimed inequality becomes $c^{3}x\le c^2{x}^2$, false whenever $0<x<c$.

Solved by gpt-5.6-sol high.