8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f9a252-61a2-491d-94d0-8470aee96942-10_689_1011_294_486}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\), where \(x \in R\), \(x > 0\)
$$\mathrm { f } ( x ) = ( 0.5 x - 8 ) \ln ( x + 1 ) \quad 0 \leq x \leq A$$
a. Find the value of \(A\).
b. Find \(\mathrm { f } ^ { \prime } ( x )\)
The curve has a minimum turning point at \(B\).
c. Show that the \(x\)-coordinate of \(B\) is a solution of the equation
$$x = \frac { 17 } { \ln ( x + 1 ) + 1 } - 1$$
d. Use the iteration formula
$$x _ { n + 1 } = \frac { 17 } { \ln \left( x _ { n } + 1 \right) + 1 } - 1$$
with \(x _ { 0 } = 5\) to find the values of \(x _ { 1 }\) and the value of \(x _ { 6 }\) giving your answers to three decimal places.