Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 16C / i / Solution

For fixed $x$ add $K\Pi (t)$ to $p(t)-f(t)$ so the resulting function also vanishes at $t=x$. Repeated Rolle gives a point $\xi$ where its $(n+1)$st derivative vanishes, yielding the formula.

Solved by gpt-5.6-sol high.