1.
$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 4$$
- Use differentiation to find \(\mathrm { f } ^ { \prime } ( x )\).
The equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval \(1.4 < x < 1.5\)
- Taking 1.4 as a first approximation to \(\alpha\), use the Newton-Raphson procedure once to obtain a second approximation to \(\alpha\). Give your answer to 3 decimal places.