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})

f (x) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

f (x, y) = 4 x^{4} + y^{2} - 2 x y + 1

f (x) = x^{3} (x - 1)^{2}

f (x, y) = 100 + x^{2} + y^{2}

f (x) = x^{4} - 32 x^{2} + 7

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