Five Point Formula

This formula can be obtained by writing out the four Taylor series of ƒ(x ± h) and ƒ(x ± 2h) up to terms of h 3 (or up to terms of h 5 to get an error estimation as well).

Five Point Formula

Input Data

x0=0, x1=1, x2=2, x3=3, x4=4 y0=1, y1=4, y2=9, y3=16, y4=25

Solution

Ans=2

This formula can be obtained by writing out the four Taylor series of ƒ(x ± h) and ƒ(x ± 2h) up to terms of h 3 (or up to terms of h 5 to get an error estimation as well).

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