17.
\includegraphics[max width=\textwidth, alt={}, center]{b1befa4f-5ef6-46e1-afb4-3a3582db7dfd-6_705_1130_623_438}
The diagram above shows a sketch of the curve \(y = 3 x - x ^ { 2 }\). The curve intersects the \(x\)-axis at the origin and at the point \(A\). The tangent to the curve at the point \(B ( 2,2 )\) intersects the \(x\)-axis at the point C .
- Find the equation of the tangent to the curve at \(B\).
- Find the area of the shaded region.