9. (3 marks) Consider the forward difference table X f(x) ?fi ?²fi ?³fi ??fi 0.3 -45 91 0.6 46 -166 -75 248 0.9 -29 82 -331 7 -83 1.2 -22 -1 6 1.5 -16 (1) Using the Newton-Gregory forward interpolation formula with the first and second forward differences gives the interpolated value: f(0.8) = _____ (2) Using the Newton-Gregory backward interpolation formula with the first-order and second-order backward differences gives the approximation to the first-order derivative f'(1.0) = _____ (3) Using the Newton-Gregory backward interpolation formula with the first-order and second-order backward differences gives the approximation to the second-order derivative f''(1.5)
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