The function \(f\) is defined for \(x \geq 0\) by \(f(x) = (4x + 1)^{\frac{3}{2}}\).

(i) Find \(f'(x)\) and \(f''(x)\).

The first, second and third terms of a geometric progression are respectively \(f(2)\), \(f'(2)\) and \(kf''(2)\).

(ii) Find the value of the constant \(k\).