(i)[7]
Find the $x$-coordinates of the stationary points in terms of $k$, and determine the nature of each one, giving reasons for your answers.
(ii)[5]
The diagram shows part of the curve for the case when $k = 1$. Show all necessary working, and find the volume produced when the shaded region, bounded by the curve, the $x$-axis, the $y$-axis and the line $x = 2$, is rotated through $360^\circ$ about the $x$-axis.