11. Let the function
$$
f(x)=\mathrm{e}^{x}\left(x^{3}-3 x+3\right)-a \mathrm{e}^{x}-x \quad (x \geqslant-2) \text {. }
$$

If the inequality $f(x) \leqslant 0$ has a solution, then the minimum value of the real number $a$ is $(\quad)$.
(A) $\frac{2}{\mathrm{e}}-1$
(B) $2-\frac{2}{\mathrm{e}}$
(C) $1+2 \mathrm{e}^{2}$
(D) $1-\frac{1}{\mathrm{e}}$
11. D.

According to the problem, $a \geqslant x^{3}-3 x+3-\frac{x}{\mathrm{e}^{x}}$. Let $h(x)=x^{3}-3 x+3-\frac{x}{\mathrm{e}^{x}}$. It is easy to find that the minimum value is $1-\frac{1}{\mathrm{e}}$. Therefore, $a \geqslant 1-\frac{1}{\mathrm{e}}$.