By sketching a suitable pair of graphs, show that the equation
$$x ^ { 3 } = 11 - 2 x$$
has exactly one real root.
Use the iterative formula
$$x _ { n + 1 } = \sqrt [ 3 ] { } \left( 11 - 2 x _ { n } \right)$$
to find the root correct to 4 significant figures. Give the result of each iteration to 6 significant figures.