Numerical Analysis | Part IB, 2001

Given fCn+1[a,b]f \in C^{n+1}[a, b], let the nn th-degree polynomial pp interpolate the values f(xi)f\left(x_{i}\right), i=0,1,,ni=0,1, \ldots, n, where x0,x1,,xn[a,b]x_{0}, x_{1}, \ldots, x_{n} \in[a, b] are distinct. Given x[a,b]x \in[a, b], find the error f(x)p(x)f(x)-p(x) in terms of a derivative of ff.

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