The function f defined by $\mathrm{f}(x)=(x+2) \mathrm{e}^{-x}$ is

The derivative of $f(x) = (x + 2)e^{-x}$ is found using the product rule, yielding $f'(x) = -e^{-x}(x + 1)$.

Since $e^{-x} > 0$ for all $x$, the sign of $f'(x)$ depends on $- (x + 1)$. Setting $f'(x) = 0$ gives the critical point $x = -1$.

For $x < -1$, $-(x + 1) > 0$, so $f'(x) > 0$ and $f(x)$ is increasing.

For $x > -1$, $-(x + 1) < 0$, so $f'(x) < 0$ and $f(x)$ is decreasing.

Thus, $f(x)$ is increasing on $(-\infty, -1)$ and decreasing on $(-1, \infty)$.

Matching the intervals, the correct choice is C.