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Question 3 (a) Given that f(-2) = 46, f(-1) = 4, f(1) = 1, f(3) = 156, and f(4) = 484, use the Lagrange interpolation formula to estimate f(0) Use four-decimal arithmetic with rounding (b) Why should the Lagrange formula be used in practice only with caution? (c) Write down the system of equations that need to be solved in order to construct the natural cubic spline function for the following data x f(x) 3.0 -5.6790 3.1 -3.6674 3.2 -2.2178 Note You need not solve the system (d) Consider the function f(x) = { 13 - 31x + 23x^2 - 5x^3 for 1 ? x ? 2 { -35 + 51x - 22x^2 + 3x^3 for 2 ? x ? 3 Is f(x) a cubic spline? Justify your answer and show all the necessary calculations

          Question 3
(a) Given that f(-2) = 46, f(-1) = 4, f(1) = 1, f(3) = 156, and f(4) = 484, use the Lagrange interpolation formula to estimate f(0) Use four-decimal arithmetic with rounding
(b) Why should the Lagrange formula be used in practice only with caution?
(c) Write down the system of equations that need to be solved in order to construct the natural cubic spline function for the following data
x f(x)
3.0 -5.6790
3.1 -3.6674
3.2 -2.2178
Note You need not solve the system
(d) Consider the function
f(x) = { 13 - 31x + 23x^2 - 5x^3 for 1 ? x ? 2
       { -35 + 51x - 22x^2 + 3x^3 for 2 ? x ? 3
Is f(x) a cubic spline? Justify your answer and show all the necessary calculations

Question 3
(a) Given that f(-2) = 46, f(-1) = 4, f(1) = 1, f(3) = 156, and f(4) = 484, use the Lagrange interpolation formula to estimate f(0) Use four-decimal arithmetic with rounding
(b) Why should the Lagrange formula be used in practice only with caution?
(c) Write down the system of equations that need to be solved in order to construct the natural cubic spline function for the following data
x f(x)
3.0 -5.6790
3.1 -3.6674
3.2 -2.2178
Note You need not solve the system
(d) Consider the function
f(x) = 13 - 31x + 23x^2 - 5x^3 for 1 ? x ? 2
-35 + 51x - 22x^2 + 3x^3 for 2 ? x ? 3
Is f(x) a cubic spline? Justify your answer and show all the necessary calculations

Added by Daniela M.

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