What is the extreme f(x)=5xe^{-5x} ?

The extreme f(x)=5xe^{-5x} is Maximum(1/5 , 1/e)

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extreme f(x)=5xe^{-5x}

extreme points

f (x) = 5 x e^{- 5 x}

Maximum (\frac{1}{5}, \frac{1}{e})

Solution steps

Find the critical points:

x = \frac{1}{5}

Domain of

5 x e^{- 5 x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < \frac{1}{5},

Decreasing

: \frac{1}{5} < x < \infty

Plug the extreme point

x = \frac{1}{5}

into

5 x e^{- 5 x} \Rightarrow y = \frac{1}{e}

Maximum (\frac{1}{5}, \frac{1}{e})

y = x^{3} - 3 x^{2} - 9 x

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

f (z) = z + z^{3} - 2 z^{2} - 4

f (x) = 1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}}

f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

What is the extreme f(x)=5xe^{-5x} ?
The extreme f(x)=5xe^{-5x} is Maximum(1/5 , 1/e)