The error of polynomial interpolation is f(z) - p(z) = f^(n)(zeta) * (z-x[0])(z-x[1])...(z-x[n-1]) / n! where f^(n) is the n-th derivative of the approximated function and zeta is some point in the interval determined by x[] and z.
Since zeta is unknown, f^(n)(zeta) cannot be calculated. But we can bound it and use the absolute value upper bound for estimates. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.
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