3.
$$\mathrm { f } ( x ) = x ^ { 2 } + \frac { 3 } { x } - 1 , \quad x < 0$$
The only real root, \(\alpha\), of the equation \(\mathrm { f } ( x ) = 0\) lies in the interval \([ - 2 , - 1 ]\).
- Taking - 1.5 as a first approximation to \(\alpha\), apply the Newton-Raphson procedure once to \(\mathrm { f } ( x )\) to find a second approximation to \(\alpha\), giving your answer to 2 decimal places.
- Show that your answer to part (a) gives \(\alpha\) correct to 2 decimal places.
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