5
20
40
200
3 A curve is defined by the parametric equations
$$x = t ^ { 3 } + 2 , \quad y = t ^ { 2 } - 1$$
3
- Find the gradient of the curve at the point where \(t = - 2\)
[0pt]
[4 marks]
3 - Find a Cartesian equation of the curve.
4 The equation \(x ^ { 3 } - 3 x + 1 = 0\) has three real roots.
4 - Show that one of the roots lies between - 2 and - 1
4 - 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]
4 - Explain why the Newton-Raphson method fails in the case when the first approximation is \(x _ { 1 } = - 1\)
[0pt]
[1 mark]