Given the following data
Which formula is useful in finding the interpolating polynomial?
Answer
Lagrange’s interpolation formula
X
1
2
5
9
f(x)
2
0
30
132
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Newton’s forward difference interpolation formula
Newton’s backward difference interpolation formula
None of the given choices

The correct answer is Lagrange’s interpolation formula.

Since the data points  = {1, 2, 5, 9} are unequally spaced, Lagrange’s interpolation formula is the appropriate method to find the interpolating polynomial. Newton’s forward and backward difference interpolation formulas are typically used when the data points are equally spaced, which is not the case here.

Therefore, Lagrange’s interpolation is best suited for this dataset.