Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 17C / c / Solution

The constant is sharp because continuous functions bounded by one can approximate $\mathrm{sgn}K$ arbitrarily closely outside an arbitrarily small interval around zero. Choose $f^{\prime \prime \prime }$ to be such an approximation and integrate three times to obtain $f\in C^3[-1,1]$. ThenNo smaller constant can therefore satisfy the inequality for every $f$.

Solved by gpt-5.6-sol high.