6 At the point \(( x , y )\), where \(x > 0\), the gradient of a curve is given by
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - \frac { 4 } { x ^ { 2 } } - 11$$
The point \(P ( 2,1 )\) lies on the curve.
- Verify that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) when \(x = 2\).
(l mark) - Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) when \(x = 2\).
- Hence state whether \(P\) is a maximum point or a minimum point, giving a reason for your answer.
- Find the equation of the curve.