A curve has equation \(y = f(x)\) and is such that \(f'(x) = 3x^{\frac{1}{2}} + 3x^{-\frac{1}{2}} - 10\).

(i) By using the substitution \(u = x^{\frac{1}{2}}\), or otherwise, find the values of \(x\) for which the curve \(y = f(x)\) has stationary points.

(ii) Find \(f''(x)\) and hence, or otherwise, determine the nature of each stationary point.