4 A curve is defined for \(x > 0\). The gradient of the curve at the point \(( x , y )\) is given by
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { x ^ { 2 } } - \frac { x } { 4 }$$
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- The curve has a stationary point \(M\) whose \(y\)-coordinate is \(\frac { 5 } { 2 }\).
- Find the \(x\)-coordinate of \(M\).
- Use your answers to parts (a) and (b)(i) to show that \(M\) is a maximum point.
- Find the equation of the curve.