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Problem: Backward, {{0,1},{1,0},{2,1},{3,10}},x=2.1 [ Calculator, Method and examples ]

Solution:
Your problem -> Backward, {{0,1},{1,0},{2,1},{3,10}},x=2.1

The value of table for X and Y

 X Y 0 1 2 3 1 0 1 10

Newton's backward differentiation method to find solution
Newton's backward differentiation table is as follows.
 X Y(X) gradY grad^2Y grad^3Y 0 1 -1 1 0 2 1 6 2 1 8 9 3 10

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

h = x_1 - x_0 = 1 - 0 = 1

q = (x - x_n) / h = (2.1 - 3) / 1 = -0.9

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