8. The curve \(C\) has equation \(y = 6 - 3 x - \frac { 4 } { x ^ { 3 } } , x \neq 0\)
- Use calculus to show that the curve has a turning point \(P\) when \(x = \sqrt { } 2\)
- Find the \(x\)-coordinate of the other turning point \(Q\) on the curve.
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- Hence or otherwise, state with justification, the nature of each of these turning points \(P\) and \(Q\).