2.
$$f ( x ) = 3 x ^ { 2 } - \frac { 11 } { x ^ { 2 } }$$
- Write down, to 3 decimal places, the value of \(\mathrm { f } ( 1.3 )\) and the value of \(\mathrm { f } ( 1.4 )\).
The equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) between 1.3 and 1.4
[0pt] - Starting with the interval [1.3, 1.4], use interval bisection to find an interval of width 0.025 which contains \(\alpha\).
- Taking 1.4 as a first approximation to \(\alpha\), apply the Newton-Raphson procedure once to \(\mathrm { f } ( x )\) to obtain a second approximation to \(\alpha\), giving your answer to 3 decimal places.