A curve has equation \(y = f(x)\) and it is given that

\(f'(x) = \left( \frac{1}{2}x + k \right)^{-2} - (1 + k)^{-2}\),

where \(k\) is a constant. The curve has a minimum point at \(x = 2\).

(a) Find \(f''(x)\) in terms of \(k\) and \(x\), and hence find the set of possible values of \(k\).

It is now given that \(k = -3\) and the minimum point is at \((2, 3\frac{1}{2})\).

(b) Find \(f(x)\).

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