9 A curve has equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = x ( 6 - x )$$
9
- \(\quad\) Find \(\mathrm { f } ^ { \prime } ( x )\)
9 - The diagram below shows the graph of \(y = \mathrm { f } ( x )\)
On the same diagram sketch the gradient function for this curve, stating the coordinates of any points where the gradient function cuts the axes.
\includegraphics[max width=\textwidth, alt={}, center]{f4f303a2-f029-42be-93a0-046b0c81e3c0-11_922_1198_1475_406}
It is given that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = ( x + 2 ) ( 2 x - 1 ) ^ { 2 }$$
and when \(x = 6 , y = 900\)
Find \(y\) in terms of \(x\)