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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`

X22.252.52.7533.253.53.754
Y914.781222.2531.59384356.656272.7591.4688113

Newton's backward differentiation method to find solution
Newton's backward differentiation table is as follows.
XY(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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