What is the extreme f(x)=-xe^{-x/4} ?

The extreme f(x)=-xe^{-x/4} is Minimum(4,-4/e)

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extreme f(x)=-xe^{-x/4}

extreme

Minimum (4, - \frac{4}{e})

Solution steps

Find the critical points:

x = 4

Domain of

- x e^{- \frac{x}{4}} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 4,

Increasing

: 4 < x < \infty

Plug the extreme point

x = 4

into

- x e^{- \frac{x}{4}} \Rightarrow y = - \frac{4}{e}

Minimum (4, - \frac{4}{e})

What is the extreme f(x)=-xe^{-x/4} ?
The extreme f(x)=-xe^{-x/4} is Minimum(4,-4/e)