2. The equation \(x ^ { 3 } - 3 x + 1 = 0\) has three real roots.
- Show that one of the roots lies between -2 and -1
- Taking \(x _ { 1 } = - 2\) as the first approximation to one of the roots, use the Newton-Raphson method to find \(x _ { 2 }\), the second approximation.
[0pt]
[3 marks] - Explain why the Newton-Raphson method fails in the case when the first approximation is \(x _ { 1 } = - 1\)