What is the extreme f(x)=xe^{-x}[0.2] ?

The extreme f(x)=xe^{-x}[0.2] is Maximum(1,(0.2)/e)

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extreme f(x)=xe^{-x}[0.2]

extreme

Maximum (1, \frac{0.2}{e})

Solution steps

Find the critical points:

x = 1

Domain of

x e^{- x} [0.2] : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

x e^{- x} [0.2] \Rightarrow y = \frac{0.2}{e}

Maximum (1, \frac{0.2}{e})

What is the extreme f(x)=xe^{-x}[0.2] ?
The extreme f(x)=xe^{-x}[0.2] is Maximum(1,(0.2)/e)