The function \(f\) is defined by \(f(x) = x^2 + \frac{k}{x} + 2\) for \(x > 0\).

(a) Given that the curve with equation \(y = f(x)\) has a stationary point when \(x = 2\), find \(k\).

(b) Determine the nature of the stationary point.

(c) Given that this is the only stationary point of the curve, find the range of \(f\).