Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 9E / b / Solution

If $f$ has $n+1$ derivatives near $x_0$, then $f(x)={\sum }_{k=0}^n{f}^{(k)}(x_0)(x-x_0{)}^k/k!+f^{(n+1)}(\xi )(x-x_0{)}^{n+1}/(n+1)!$ for some intermediate $\xi$.

Solved by gpt-5.6-sol high.