Chapter 3.1, Problem 15ES

(a)

To determine

The approximate $f\left(0.25\right)$ using linear interpolation with $x_0=0$ and $x_1=0.5$.

(b)

To determine

The approximate $f\left(0.75\right)$ using linear interpolation with $x_0=0.5$ and $x_1=1$.

(c)

To determine

The approximate $f\left(0.25\right)$ and $f\left(0.75\right)$ using second interpolation polynomial with $x_0=0$, $x_1=1$ and $x_2=2$.

(d)

To determine

The approximation is better and why.