Question 1 From the table below, construct the backward difference table hence obtained using the Newton interpolation formular, $f(4.5)$. \begin{tabular}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 3 & 12 & 81 & 200 & 100 & 8 \\ \hline \end{tabular} Question 2 Construct Newton's divided difference formular for the following data and evaluate $f(6)$. \begin{tabular}{|c|c|c|c|c|} \hline x & 1 & 2 & 7 & 8 \\ \hline f(x) & 1 & 5 & 5 & 4 \\ \hline \end{tabular}
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