A curve is such that \(\frac{dy}{dx} = x^{\frac{1}{2}} - x^{-\frac{1}{2}}\). The curve passes through the point \((4, \frac{2}{3})\).

(i) Find the equation of the curve.

(ii) Find \(\frac{d^2y}{dx^2}\).

(iii) Find the coordinates of the stationary point and determine its nature.