10
\includegraphics[max width=\textwidth, alt={}, center]{8da9e73a-3126-471b-b904-25e3c156f6bf-3_682_1319_1525_413}
Points \(A ( 2,9 )\) and \(B ( 3,0 )\) lie on the curve \(y = 9 + 6 x - 3 x ^ { 2 }\), as shown in the diagram. The tangent at \(A\) intersects the \(x\)-axis at \(C\). Showing all necessary working,
- find the equation of the tangent \(A C\) and hence find the \(x\)-coordinate of \(C\),
- find the area of the shaded region \(A B C\).
[0pt]
[Question 11 is printed on the next page.]