The curve \(C\) has equation \(y = k x ^ { 3 } - x ^ { 2 } + x - 5\), where \(k\) is a constant.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
The point \(A\) with \(x\)-coordinate \(- \frac { 1 } { 2 }\) lies on \(C\). The tangent to \(C\) at \(A\) is parallel to the line with equation \(2 y - 7 x + 1 = 0\).
Find
- the value of \(k\),
- the value of the \(y\)-coordinate of \(A\).