10. A curve has equation \(y = \mathrm { f } ( x ) , x > 0\)
Given that
- \(\mathrm { f } ^ { \prime } ( x ) = a x - 12 x ^ { \frac { 1 } { 3 } }\), where \(a\) is a constant
- \(\mathrm { f } ^ { \prime \prime } ( x ) = 0\) when \(x = 27\)
- the curve passes through the point \(( 1 , - 8 )\)
- find the value of \(a\).
- Hence find \(\mathrm { f } ( x )\).