- The curve \(C\) has equation \(y = \mathrm { f } ( x )\)
The curve
- passes through the point \(P ( 3 , - 10 )\)
- has a turning point at \(P\)
Given that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x ^ { 3 } - 9 x ^ { 2 } + 5 x + k$$
where \(k\) is a constant,
- show that \(k = 12\)
- Hence find the coordinates of the point where \(C\) crosses the \(y\)-axis.