(a)[3]
Find an expression for $\frac{dy}{dx}$ and determine, with a reason, whether the curve has stationary points at all.
(b)[4]
Find the volume of the solid formed when the region enclosed by the curve, the coordinate axes and the line $x = 1$ is rotated through $360^{\circ}$ about the $x$-axis.
(c)[4]
Find the set of $k$ values for which the line $y = x + k$ meets the curve at two distinct points.