CUET Preparation Today
The function f defined by $f(x)=(x+2) e^{-x}$ is |
decreasing for all x decreasing in $(-\infty,-1)$ and increasing in $(-1, \infty)$ increasing for all x decreasing in $(-1, \infty)$ and increasing in $(-\infty,-1)$ |
decreasing in $(-1, \infty)$ and increasing in $(-\infty,-1)$ |
We have, $f(x)=(x+2) e^{-x} \Rightarrow f^{\prime}(x)=e^{-x}-(x+2) e^{-x}=-(x+1) e^{-x}$ ∴ $f^{\prime}(x)<0$ $\Rightarrow -(x+1) e^{-x}<0 \Rightarrow-(x+1)<0 \Rightarrow x+1>0 \Rightarrow x>-1$ Hence, f(x) is decreasing in $(-1, \infty)$ and increasing in $(-\infty,-1)$. |
