(i)[5]
Show that the area of the shaded region enclosed by the curve, the $x$-axis and the line $x = 3$ is $2 - \frac{17}{e^3}$.
(ii)[4]
Find the $x$-coordinate of maximum point $M$ on the curve.
(iii)[2]
Find the $x$-coordinate of point $P$ where the tangent to the curve passes through the origin.