Bài giải:

Chọn A.

(I):$y'=(-{{x}^{3}}+3{{x}^{2}}-3x+1)'=-3{{x}^{2}}+6x-3=-3{{(x-1)}^{2}}\le 0,\text{ }\forall x\in \mathbb{R}$;

(II):$y'=(\sin x-2x)'=\cos x-2<0,\forall x\in \mathbb{R}$;

(III) ${y}'=-{{\left( \sqrt{{{x}^{3}}+2} \right)}^{\prime }}=-\frac{3{{x}^{2}}}{2\sqrt{{{x}^{3}}+2}}\le 0,\forall x\in \left( -\sqrt[3]{2};+\infty  \right)$;

(IV) $y'={{\left( \frac{x-2}{1-x} \right)}^{\prime }}={{\left( \frac{x-2}{-x+1} \right)}^{\prime }}=-\frac{1}{{{(1-x)}^{2}}}<0,\text{ }\forall x\ne 1$