Mark the correct alternative in the following:

Question:

Mark the correct alternative in the following:

The function $f(x)=x^{2} e^{-x}$ is monotonic increasing when

A. $x \in R-[0,2]$

B. $0

C. $2

D. $x<0$

Solution:

$f(x)=x^{2} e^{-x}$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=x \mathrm{e}^{-\mathrm{x}}(2-\mathrm{x})=\mathrm{f}^{\prime}(\mathrm{x})$

for

$f^{\prime}(x)=0$

$\Rightarrow x^{2} e^{-x}=0$

$\Rightarrow x(2-x)=0$

$x=2, x=0$

$f(x)$ is increasing in $(0,2)$

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