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

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

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

extreme points

f (x) = 2 x e^{- x}

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

Solution steps

Find the critical points:

x = 1

Domain of

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

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

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

x^{\frac{2}{3}} (\frac{5}{2} - x)

f (x) = 2 x^{5} + 5 x^{4}

f (x, y) = 3 x^{2} - x y + 2 y^{3}

f (x) = 89 e^{x^{4}} + 11

f (x) = x - \frac{1}{x}

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