Find the equation of a cubic curve which passes through the points (0, 2), (1, 3), (2, 12) and (5, 147) using?

Question

Find the equation of a cubic curve which passes through the points (0, 2), (1, 3), (2, 12) and (5, 147) using Divided Difference Formula.(Math, Numerical \Analysis)

Answer 1

0, 2

1, 3, 1

2, 12, 9, 4

5, 147, 45, 9, 1

y = 2 + x(1) + 4x(x - 1) + x(x - 1)(x - 2)

y = 2 + x + 4x^2 - 4x + x(x^2 - 3x + 2)

y = 2 + 4x^2 - 3x + x^3 - 3x^2 + 2x

y = 2 - 3x + 2x - 3x^2 + 4x^2 + x^3

y = 2 - x + x^2 + x^3