Example 3: Using the data | x_i | 4 | 6 | 8 | 10 | | :--- | :--- | :--- | :--- | :--- | | f(x_i) | 1 | 3 | 8 | 20 | a) Find f (4.5), using Newton's Forward Difference Formula for interpolation. b) Find f (9), using Newton's Backward Difference Formula for interpolation.
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Given the data points (10, 20), we can't apply these formulas directly because they require at least two data points to calculate the differences. Newton's Forward Difference Formula is used when the value of x is close to the first value in the data set, while Show more…
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