By sketching suitable graphs, show that the equation \(\mathrm { e } ^ { - \frac { 1 } { 2 } x } = 4 - x ^ { 2 }\) has one positive root and one negative root.
Verify by calculation that the negative root lies between - 1 and - 1.5 .
Use the iterative formula \(x _ { n + 1 } = - \sqrt { } \left( 4 - e ^ { - \frac { 1 } { 2 } x _ { n } } \right)\) to determine this root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.