9. A curve has the equation \(y = x ^ { 3 } - 5 x ^ { 2 } + 7 x\).
- Show that the curve only crosses the \(x\)-axis at one point.
The point \(P\) on the curve has coordinates \(( 3,3 )\).
- Find an equation for the normal to the curve at \(P\), giving your answer in the form \(a x + b y = c\), where \(a , b\) and \(c\) are integers.
The normal to the curve at \(P\) meets the coordinate axes at \(Q\) and \(R\).
- Show that triangle \(O Q R\), where \(O\) is the origin, has area \(28 \frac { 1 } { 8 }\).