Q1. Apply the Newton-divided difference formula to interpolate the first and second derivative of the following data at $x = 3$ and $x = 6$. $i$ 0 1 2 3 4 $x_i$ 2 6 13 25 37 $y_i = f(x_i)$ -10 50 120 264 360
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The divided differences for the first derivative can be calculated using the formula: f[xi, xi+1] = (f(xi+1) - f(xi)) / (xi+1 - xi) For the given data, the divided differences for the first derivative are: f[0, 1] = (6 - 2) / (1 - 0) = 4 f[1, 2] = (13 - 6) / Show more…
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