What is the extreme f(x)=4xe^{-2x} ?

The extreme f(x)=4xe^{-2x} is Maximum(1/2 , 2/e)

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extreme f(x)=4xe^{-2x}

extreme

Maximum (\frac{1}{2}, \frac{2}{e})

Solution steps

Find the critical points:

x = \frac{1}{2}

Domain of

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

Find intervals:

Increasing

: - \infty < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug the extreme point

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, \frac{2}{e})

What is the extreme f(x)=4xe^{-2x} ?
The extreme f(x)=4xe^{-2x} is Maximum(1/2 , 2/e)