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- Lagrange: P(x) = Σ f(xₖ)Lₖ(x), Lₖ(x) = Π_{i≠k} (x − xᵢ)/(xₖ − xᵢ). Degree ≤ n through n + 1 points.
- Error: f(x) − P(x) = f⁽ⁿ⁺¹⁾(ξ)/(n + 1)! · Π(x − xᵢ).
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Find the linear Lagrange polynomial through (2, 4) and (5, 1).
P(x) = 4(x − 5)/(2 − 5) + 1(x − 2)/(5 − 2) = −(4/3)(x − 5) + (1/3)(x − 2) = −x + 6.
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