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\includegraphics[max width=\textwidth, alt={}, center]{13cfb59a-7781-4786-a625-919b01a2a4f0-4_643_570_849_790}
The diagram shows part of the curve \(y = \frac { 8 } { \sqrt { } x } - x\) and points \(A ( 1,7 )\) and \(B ( 4,0 )\) which lie on the curve. The tangent to the curve at \(B\) intersects the line \(x = 1\) at the point \(C\).
- Find the coordinates of \(C\).
- Find the area of the shaded region.