12.
$$f ( x ) = 3 ^ { x } - x - 6$$
- Show that \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) between \(x = 1\) and \(x = 2\).
- Starting with the interval (1,2), use interval bisection three times to find an interval of width 0.125 which contains \(\alpha\).
[0pt]
[*P4 June 2003 Qn 4]