11 A curve has equation \(y = ( k x - 3 ) ^ { - 1 } + ( k x - 3 )\), where \(k\) is a non-zero constant.
- Find the \(x\)-coordinates of the stationary points in terms of \(k\), and determine the nature of each stationary point, justifying your answers.
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The diagram shows part of the curve for the case when \(k = 1\). Showing all necessary working, find the volume obtained when the region between the curve, the \(x\)-axis, the \(y\)-axis and the line \(x = 2\), shown shaded in the diagram, is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
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