5 The point \(P ( 2,8 )\) lies on a curve, and the point \(M\) is the only stationary point of the curve.
The curve has equation \(y = 6 + 2 x - \frac { 8 } { x ^ { 2 } }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Show that the normal to the curve at the point \(P ( 2,8 )\) has equation \(x + 4 y = 34\).
- Show that the stationary point \(M\) lies on the \(x\)-axis.
- Hence write down the equation of the tangent to the curve at \(M\).
- The tangent to the curve at \(M\) and the normal to the curve at \(P\) intersect at the point \(T\). Find the coordinates of \(T\).