11. The curve \(C\) has equation
$$y = x ^ { 3 } - 2 x ^ { 2 } - x + 9 , \quad x > 0$$
The point \(P\) has coordinates (2, 7).
- Show that \(P\) lies on \(C\).
- Find the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
The point \(Q\) also lies on \(C\).
Given that the tangent to \(C\) at \(Q\) is perpendicular to the tangent to \(C\) at \(P\), - show that the \(x\)-coordinate of \(Q\) is \(\frac { 1 } { 3 } ( 2 + \sqrt { 6 } )\).