9.
\includegraphics[max width=\textwidth, alt={}]{0744b3cf-2941-45cb-b6df-2aaf44588e5c-3_592_771_683_541}
The diagram shows the curve \(C\) with equation \(y = 3 x - 4 \sqrt { x } + 2\) and the tangent to \(C\) at the point \(A\).
Given that \(A\) has \(x\)-coordinate 4,
- show that the tangent to \(C\) at \(A\) has the equation \(y = 2 x - 2\).
The shaded region is bounded by \(C\), the tangent to \(C\) at \(A\) and the \(y\)-axis.
- Find the area of the shaded region.