[填空题]
Let $f(x)=\frac{\ln \left(8 x^{3}\right)}{k x}$ where x$\lt$0,$k \in \mathbb{R}^{+}$ .
1. Show that $f^{\prime}(x)=\frac{3-\ln \left(8 x^{3}\right)}{k x^{2}} $.
The graph of f has exactly one maximum point A .
2. Find the x -coordinate of A.
The second derivative of f is given by $ f^{\prime \prime}(x)=\frac{2 \ln \left(8 x^{3}\right)-9}{k x^{3}}$ . The graph of f has exactly one point of inflexion B ,
3. Show that the x -coordinate of B is $\frac{e^{3 / 2}}{2}$ .
The region R is enclosed by the graph of f , the x -axis, and the vertical lines through the maximum point A and the point of inflexion B .
$\text { 4. Given that the area of } R \text { is } 5 \text {, find the value of } k \text {. }$
