(i)[6]
At the point $A$, the tangent to the curve $y = x^3 - 9x^2 + 24x - 12$ is parallel to the line $y = 2 - 3x$. Find the equation of the tangent at $A$.
(ii)[2]
The function $f$ is given by $f(x) = x^3 - 9x^2 + 24x - 12$ for $x > k$, where $k$ is a constant. Find the smallest value of $k$ for $f$ to be an increasing function.
(b(ii))[2]
The function $f$ is defined by $f(x) = x^3 - 9x^2 + 24x - 12$ for $x > k$, with $k$ a constant. Find the least value of $k$ that makes $f$ increasing.