Exercise 6.3.20

Follow the method after Theorem 6.12.

1.

The linear function is $-2t+\frac{5}{2}$ with error $E=1$. The quadratic function is $\frac{1}{3}{t}^2-\frac{4}{3}t+2$ with the error $E=0$.

2.

The linear function is $\frac{5}{4}t+\frac{11}{20}$ with error $E=\frac{3}{10}$. The quadratic function is $\frac{1}{56}{t}^2+\frac{15}{14}+\frac{239}{280}$ with the error $E=\frac{8}{35}$.

3.

The linear function is $-\frac{9}{5}t+\frac{4}{5}$ with error $E=\frac{2}{5}$. The quadratic function is $-\frac{1}{7}{t}^2-\frac{9}{5}t+\frac{38}{35}$ with the error $E=\frac{4}{35}$.