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Problem: Divided Difference, 2x^3-4x+1, [2,4], x=2.1, h=0.25 [ Calculator, Method and examples ]

Solution:
Your problem -> Divided Difference, 2x^3-4x+1, [2,4], x=2.1, h=0.25

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

The value of table for X and Y

 X Y 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 9 14.7812 22.25 31.5938 43 56.6562 72.75 91.4688 113

Numerical divided differences method to find solution
Newton's divided difference table is as follows.
 X Y(X) 1^(st) order 2^(nd) order 3^(rd) order 4^(th) order 2 9 23.125 2.25 14.7812 13.5 29.875 2 2.5 22.25 15 0 37.375 2 2.75 31.5938 16.5 0 45.625 2 3 43 18 0 54.625 2 3.25 56.6562 19.5 0 64.375 2 3.5 72.75 21 0 74.875 2 3.75 91.4688 22.5 86.125 4 113

The value of x at you want to find the f(x) : x = 2.1

Y(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]

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