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\includegraphics[max width=\textwidth, alt={}, center]{3b527397-7781-41e9-8218-57277cc977bf-4_686_805_950_669} The diagram shows the curve \(y = x ^ { 3 } - 6 x ^ { 2 } + 9 x\) for \(x \geqslant 0\). The curve has a maximum point at \(A\) and a minimum point on the \(x\)-axis at \(B\). The normal to the curve at \(C ( 2,2 )\) meets the normal to the curve at \(B\) at the point \(D\).

1. Find the coordinates of \(A\) and \(B\).
2. Find the equation of the normal to the curve at \(C\).
3. Find the area of the shaded region. \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }