11 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 ( 3 x - 5 ) ^ { 3 } - k x ^ { 2 }\), where \(k\) is a constant. The curve has a stationary point at \(( 2 , - 3.5 )\).
- Find the value of \(k\).
................................................................................................................................................. . . - Find the equation of the curve.
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- Determine the nature of the stationary point at \(( 2 , - 3.5 )\).