Page 3 of 6 2. (30 points) The following data were measured precisely: f(x) x 1 4 2 3 3 8 4 1 2 and x = 3. a) (3 points)

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Page 3 Of 6 2 30 Points The Following Data Were Measured Precisely F X X 1 4 2 3 3 8 4 1 2 And X 3 A 3 Points 1 (22.06 KiB) Viewed 58 times

Page 3 of 6 2. (30 points) The following data were measured precisely: f(x) x 1 4 2 3 3 8 4 1 2 and x = 3. a) (3 points) Calculate f2.2) using first-order Newton's interpolating polynomial. Use data points at x = b) (9 points) Calculate ſ(2.2) using third-order Newton's interpolating polynomial. Use all data points c) (18 points) (14 points) Fit natural cubic splines to the data (i.e., develop the cubic splines for each interval), then (4 points) predict the function value at r= 2.2 and x = 3.6.