10. The curve \(C\) has the equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = ( x + 2 ) ^ { 3 }$$
- Sketch the curve \(C\), showing the coordinates of any points of intersection with the coordinate axes.
- Find \(\mathrm { f } ^ { \prime } ( x )\).
The straight line \(l\) is the tangent to \(C\) at the point \(P ( - 1,1 )\).
- Find an equation for \(l\).
The straight line \(m\) is parallel to \(l\) and is also a tangent to \(C\).
- Show that \(m\) has the equation \(y = 3 x + 8\).