The tangent to the curve \(y = x ^ { 3 } - 9 x ^ { 2 } + 24 x - 12\) at a point \(A\) is parallel to the line \(y = 2 - 3 x\). Find the equation of the tangent at \(A\).
The function f is defined by \(\mathrm { f } ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 24 x - 12\) for \(x > k\), where \(k\) is a constant. Find the smallest value of \(k\) for f to be an increasing function.