8 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - x ^ { 2 } + 5 x - 4\).
- Find the \(x\)-coordinate of each of the stationary points of the curve.
- Obtain an expression for \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and hence or otherwise find the nature of each of the stationary points.
- Given that the curve passes through the point \(( 6,2 )\), find the equation of the curve.