What is the extreme f(x)=-xe^{-x/2} ?

The extreme f(x)=-xe^{-x/2} is Minimum(2,-2/e)

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extreme f(x)=-xe^{-x/2}

extreme

Minimum (2, - \frac{2}{e})

Solution steps

Find the critical points:

x = 2

Domain of

- x e^{- \frac{x}{2}} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 2,

Increasing

: 2 < x < \infty

Plug the extreme point

x = 2

into

- x e^{- \frac{x}{2}} \Rightarrow y = - \frac{2}{e}

Minimum (2, - \frac{2}{e})

What is the extreme f(x)=-xe^{-x/2} ?
The extreme f(x)=-xe^{-x/2} is Minimum(2,-2/e)