# 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).

#### Input Data

$$x_0=0,\ x_1=1,\ x_2=2,\ x_3=3,\ x_4=4$$ $$y_0=1,\ y_1=4,\ y_2=9,\ y_3=16,\ y_4=25$$

#### 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).

A.