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

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

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

extreme points

f (x) = 4 x e^{- x}

Maximum (1, \frac{4}{e})

Solution steps

Find the critical points:

x = 1

Domain of

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

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

Maximum (1, \frac{4}{e})

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