4 A curve has equation \(y = \frac { 1 } { x ^ { 2 } } + 4 x\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- The point \(P ( - 1 , - 3 )\) lies on the curve. Find an equation of the normal to the curve at the point \(P\).
- Find an equation of the tangent to the curve that is parallel to the line \(y = - 12 x\).
[0pt]
[5 marks]