Question

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

• A. Decreasing for all $x$
• B. Decreasing in $(-\infty ,-1)$ and increasing in $(-1,\infty )$
• C. Increasing for all $x$
• D. Decreasing in $(-1,\infty )$ and increasing in $(-\infty ,-1)$

Answer 1

Answer: (D)

Decreasing in $(-1,\infty )$ and increasing in $(-\infty ,-1)$

Given, $f\left(x\right)=(x+2)e^{-x}$
$f^{\prime }\left(x\right)=-(x+2)e^{-x}+e^{-x}$
As $e^{-x}$ is positive for all $x$
$f\left(x\right)$ is decreasing in $(-1,\infty )$ and increasing in $(-1,-\infty )$.