10 The equation of a curve is such that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = 6 x ^ { 2 } - \frac { 4 } { x ^ { 3 } }\). The curve has a stationary point at \(\left( - 1 , \frac { 9 } { 2 } \right)\).
- Determine the nature of the stationary point at \(\left( - 1 , \frac { 9 } { 2 } \right)\).
- Find the equation of the curve.
- Show that the curve has no other stationary points.
- A point \(A\) is moving along the curve and the \(y\)-coordinate of \(A\) is increasing at a rate of 5 units per second.
Find the rate of increase of the \(x\)-coordinate of \(A\) at the point where \(x = 1\).
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