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The diagram shows the curve with equation \(\mathrm { y } = 2 \mathrm { x } ^ { - \frac { 2 } { 3 } } - 3 \mathrm { x } ^ { - \frac { 1 } { 3 } } + 1\) for \(x > 0\). The curve crosses the \(x\)-axis at points \(A\) and \(B\) and has a minimum point \(M\).
- Find the exact coordinates of \(M\).
- Find the area of the region bounded by the curve and the line segment \(A B\).
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