Question: 1. (a) Generate an O(h2) (second-order) approximation to the first derivative of some function f(x) using 3 points, x0 x1 and x2 using the polynomial

1. (a) Generate an O(h2) (second-order) approximation to the first derivative of some function f(x) using 3 points, x0 x1 and x2 using the polynomial interpolation approach in lagrange form. Give the finite formulas for each of the points x0, x1, and x2. Assume they are equally spaced, with spacing h.

(b) Using the error term for polynomial interpolation, show that the error above is O(h2).

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