The diagram shows part of the curve \(y = \frac{2}{(3 - 2x)^2} - x\) and its minimum point \(M\), which lies on the \(x\)-axis.

(a) Find expressions for \(\frac{dy}{dx}\), \(\frac{d^2y}{dx^2}\) and \(\int y \, dx\).

(b) Find, by calculation, the \(x\)-coordinate of \(M\).

(c) Find the area of the shaded region bounded by the curve and the coordinate axes.