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3. The set of the following data points is given days x| 14 [ 22 [ 30 | 38 y | 320 | 490 [

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3. The set of the following data points is given days x| 14 [ 22 [ 30 | 38 y | 320 | 490 [ 540 | 380 (a) Determine the natural cubic splines that fit the data. (b) Determine the clamped-clamped splines that fit the data () Determine the interpolated value of y for x = 27 both from (a) and (b). (d) Plot of the data points and the interpolating polynomials

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