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The function $\mathrm{f}(\mathrm{x})$ is defined by $\mathrm{f}(\mathrm{x})=(\mathrm{x}+2) \mathrm{e}^{-\mathrm{x}}$ is
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monotonically decreasing in $(-1, \infty)$ and monotonically increasing in $(-\infty,-1)$
$\begin{aligned} & \mathrm{f}(\mathrm{x})=(\mathrm{x}+2) \mathrm{e}^{-\mathrm{x}} \Rightarrow \mathrm{f} \mathrm{P}^{\prime}(\mathrm{x})=\mathrm{e}^{-\mathrm{x}}-(\mathrm{x}+2) \mathrm{e}^{-\mathrm{x}}=\mathrm{e}^{-\mathrm{x}}(1-\mathrm{x}-2) \\ & \Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=-\mathrm{e}^{-\mathrm{x}}(1+\mathrm{x}) \text { sign scheme }\end{aligned}$
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