6 The curve with equation \(y = 2 x - 8 x ^ { \frac { 1 } { 2 } }\) has a minimum point at \(A\) and intersects the positive \(x\)-axis at \(B\).
- Find the coordinates of \(A\) and \(B\).
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The diagram shows the curve with equation \(\mathrm { y } = 2 \mathrm { x } - 8 \mathrm { x } ^ { \frac { 1 } { 2 } }\) and the line \(A B\). It is given that the equation of \(A B\) is \(y = \frac { 2 x - 32 } { 3 }\).
Find the area of the shaded region between the curve and the line.