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

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Your problem -> Numerical Differentiation, 2x^3-4x+1, [2,4], x=2.1, h=0.25

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

Numerical differentiation method to find solution.
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 forward differentiation table is as follows.
 X Y(X) DeltaY Delta^2Y Delta^3Y Delta^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 f(x) : x_0 = 2.1

h = x_1 - x_0 = 2.25 - 2 = 0.25

t = (x_0 - 2)/h = (2.1 - 2)/0.25 = 0.4

[(dy)/(dx)]_(x=x_0) = 1/h * ( Delta Y_0 + (2t-1)/(2!) * Delta^2 Y_0 + (3t^2-6t+2)/(3!) * Delta^3 Y_0 + (4t^3-18t^2+22t-6)/(4!) * Delta^4 Y_0)

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