It is given that \(y=\mathrm{f}(x)\), where \(\mathrm{f}(x)=(2 x-5)(x-1)^{2}\). (a) Find the coordinates of the stationary points on the curve \(y=\mathrm{f}(x)\).

(b) On the axes, sketch the graph of \(y=\mathrm{f}(x)\), stating the intercepts with the axes.

(c) Hence find the values of \(k\) for which \(\mathrm{f}(x)=k\) has exactly one solution.