3.
$$\mathrm { g } ( x ) = \frac { 3 x ^ { 3 } + 8 x ^ { 2 } - 3 x - 6 } { x ( x + 3 ) } \equiv A x + B + \frac { C } { x } + \frac { D } { x + 3 }$$
- Find the values of the constants \(A , B , C\) and \(D\).
A curve has equation
$$y = g ( x ) \quad x > 0$$
Using the answer to part (a),
- find \(\mathrm { g } ^ { \prime } ( x )\).
- Hence, explain why \(\mathrm { g } ^ { \prime } ( x ) > 3\) for all values of \(x\) in the domain of g .