牛顿插值公式与拉格朗日插值的余项

Suppose that $n\geq 0$ ,and that $f$ is a real-valued function,defined and continuous on the closed interval $[a,b]$,such that the derivative of $f$ of order $n+1$ exists and is continuous on $[a,b]$.Then,given that $x_{n+1}\in [a,b]$,there exists $\xi=\xi(x_{n+1})$ in $(a,b)$ such that Suppose that $n\geq 0$ ,and that $f$ is a real