The diagram shows a curve with equation \(y = 4x^{\frac{1}{2}} - 2x\) for \(x \geq 0\), and a straight line with equation \(y = 3 - x\). The curve crosses the x-axis at \(A(4, 0)\) and crosses the straight line at \(B\) and \(C\).

(a) Find, by calculation, the x-coordinates of \(B\) and \(C\).

(b) Show that \(B\) is a stationary point on the curve.

(c) Find the area of the shaded region.