Question: Show that Lagranges interpolation formula for cubic interpolation is Use this formula to find a cubic polynomial that fits the function f given in the

Show that Lagrange’s interpolation formula for cubic interpolation is

f(x) = (x-x)(x-x)(x (xox)(xox)(x x3) - x) - + (x-x)(x-x)(x - x) + -fi (x - x0)(x - x)(x - x3) -fo

Use this formula to find a cubic polynomial that fits the function f given in the following table:

x fox) -1 - 1 0 0 1 1 2 8

Draw the graph of the cubic for –1 1/3.

f(x) = (x-x)(x-x)(x (xox)(xox)(x x3) - x) - + (x-x)(x-x)(x - x) + -fi (x - x0)(x - x)(x - x3) -fo (x-x)(x-x)(x - x) (x-x)(x-x)(x -$ x3) - (x - x)(x-x)(x - x) -f3 + - (x3 - x)(x3x)(xz - x)`

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