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 \(C\).

(i) Find the coordinates of \(C\).

(ii) Find the area of the shaded region.