7. The curve with equation \(y = x ^ { \frac { 5 } { 2 } } \ln \frac { x } { 4 } , x > 0\) crosses the \(x\)-axis at the point \(P\).
- Write down the coordinates of \(P\).
The normal to the curve at \(P\) crosses the \(y\)-axis at the point \(Q\).
- Find the area of triangle \(O P Q\) where \(O\) is the origin.
The curve has a stationary point at \(R\).
- Find the \(x\)-coordinate of \(R\) in exact form.