4. \(f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 5 x - 3\)
The equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval ( 2,3 ).
- Use linear interpolation on the end points of this interval to obtain an approximation for \(\alpha\).
- Taking 2.5 as a first approximation to \(\alpha\), apply the Newton - Raphson procedure once to \(\mathrm { f } ( x )\) to obtain a second approximation to \(\alpha\). Give your answer to 2 decimal places.