4. Given that \(\alpha\) is the only real root of the equation
$$x ^ { 3 } - x ^ { 2 } - 6 = 0$$
- show that \(2.2 < \alpha < 2.3\)
- Taking 2.2 as a first approximation to \(\alpha\), apply the Newton-Raphson procedure once to \(\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 6\) to obtain a second approximation to \(\alpha\), giving your answer to 3 decimal places.
[0pt] - Use linear interpolation once on the interval [2.2, 2.3] to find another approximation to \(\alpha\), giving your answer to 3 decimal places.