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

Solution:
Your problem -> Backward, 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

Newton's backward differentiation method to find solution
Newton's backward differentiation table is as follows.
 X Y(X) gradY grad^2Y grad^3Y grad^4Y 2 9 5.7812 2.25 14.7812 1.6875 7.4688 0.1875 2.5 22.25 1.875 0 9.3438 0.1875 2.75 31.5938 2.0625 0 11.4062 0.1875 3 43 2.25 0 13.6562 0.1875 3.25 56.6562 2.4375 0 16.0938 0.1875 3.5 72.75 2.625 0 18.7188 0.1875 3.75 91.4688 2.8125 21.5312 4 113

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

h = x_1 - x_0 = 2.25 - 2 = 0.25

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