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\includegraphics[max width=\textwidth, alt={}, center]{71fe6352-e0dc-4c3a-8b54-99709a1782ca-4_602_899_248_625}
The diagram shows part of the curve \(y = x + \frac { 4 } { x }\) which has a minimum point at \(M\). The line \(y = 5\) intersects the curve at the points \(A\) and \(B\).
- Find the coordinates of \(A , B\) and \(M\).
- Find the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.