9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a7285542-c32a-45b1-921b-d528676ad6b5-4_620_872_895_504}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 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 positive coordinate axes.
- Find the area of the shaded region.