A curve has equation \(y = f(x)\), and it is given that \(f'(x) = 2x^2 - 7 - \frac{4}{x^2}\).

(a) Given that \(f(1) = -\frac{1}{3}\), find \(f(x)\).

(b) Find the coordinates of the stationary points on the curve.

(c) Find \(f''(x)\).

(d) Hence, or otherwise, determine the nature of each of the stationary points.