Find Solution of an equation 2x^3-4x+1 using Newton's Divided Difference Interpolation formula
x1 = 2 and x2 = 4
x = 3.8
Step value (h) = 0.5
Finding f(2)

Solution:
Equation is `f(x)=2x^3-4x+1`.

The value of table for `x` and `y`

x	2	2.5	3	3.5	4
y	9	22.25	43	72.75	113

Numerical divided differences method to find solution

Newton's divided difference table is

x	y	`1^(st)` order	`2^(nd)` order	`3^(rd)` order	`4^(th)` order
2	9
		26.5
2.5	22.25		15
		41.5		2
3	43		18		0
		59.5		2
3.5	72.75		21
		80.5
4	113

The value of `x` at you want to find the `f(x) : x = 3.8`

Newton's divided difference interpolation formula is
`f(x)=y_0 +(x-x_0) f[x_0, x_1]+(x-x_0)(x-x_1) f[x_0, x_1, x_2]+(x-x_0)(x-x_1)(x-x_2) f[x_0, x_1, x_2, x_3]+(x-x_0)(x-x_1)(x-x_2)(x-x_3) f[x_0, x_1, x_2, x_3, x_4]`

`y(3.8) = 9 + (3.8 -2) xx 26.5 + (3.8 -2)(3.8 -2.5) xx 15 + (3.8 -2)(3.8 -2.5)(3.8 -3) xx 2 + (3.8 -2)(3.8 -2.5)(3.8 -3)(3.8 -3.5) xx 0`

`y(3.8) = 9 + (1.8) xx 26.5 + (1.8)(1.3) xx 15 + (1.8)(1.3)(0.8) xx 2 + (1.8)(1.3)(0.8)(0.3) xx 0`

`y(3.8) = 9 +47.7 +35.1 +3.744 +0`

`y(3.8) = 95.544`


Solution of divided difference interpolation method `y(3.8) = 95.544`

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