9 For all real values of \(x\) and \(y\) the surface \(S\) has equation \(z = 4 x ^ { 2 } + 4 x y + y ^ { 2 } + 6 x + 3 y + k\), where \(k\) is a constant and an integer.
- Find \(\frac { \partial z } { \partial x }\) and \(\frac { \partial z } { \partial y }\).
- Determine the smallest value of the integer \(k\) for which the whole of \(S\) lies above the \(x - y\) plane.