4.
$$f ( x ) = - x ^ { 3 } + 3 x ^ { 2 } - 1$$
- Show that the equation \(\mathrm { f } ( x ) = 0\) can be rewritten as
$$x = \sqrt { } \left( \frac { 1 } { 3 - x } \right)$$
- Starting with \(x _ { 1 } = 0.6\), use the iteration
$$\left. x _ { n + 1 } = \sqrt { ( } \frac { 1 } { 3 - x _ { n } } \right)$$
to calculate the values of \(x _ { 2 } , x _ { 3 }\) and \(x _ { 4 }\), giving all your answers to 4 decimal places.
- Show that \(x = 0.653\) is a root of \(\mathrm { f } ( x ) = 0\) correct to 3 decimal places.