10.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{9e4e1626-238b-4afd-b81c-68c5ab1624c2-16_525_928_312_621}
\end{figure}
Figure 2 shows part of the curve \(C\) with equation
$$y = 9 - 2 x - \frac { 2 } { \sqrt { x } } , \quad x > 0$$
The point \(A ( 1,5 )\) lies on \(C\) and the curve crosses the \(x\)-axis at \(B ( b , 0 )\), where \(b\) is a constant and \(b > 0\).
- Verify that \(b = 4\).
The tangent to \(C\) at the point \(A\) cuts the \(x\)-axis at the point \(D\), as shown in Fig. 2 .
- Show that an equation of the tangent to \(C\) at \(A\) is \(y + x = 6\).
- Find the coordinates of the point \(D\).
The shaded region \(R\), shown in Fig. 2, is bounded by \(C\), the line \(A D\) and the \(x\)-axis.
- Use integration to find the area of \(R\).
- continued
- continued