What is the extreme f(x)=3xe^{-x} ?

The extreme f(x)=3xe^{-x} is Maximum(1, 3/e)

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extreme f(x)=3xe^{-x}

extreme points

f (x) = 3 x e^{- x}

Maximum (1, \frac{3}{e})

Solution steps

Find the critical points:

x = 1

Domain of

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

3 x e^{- x} \Rightarrow y = \frac{3}{e}

Maximum (1, \frac{3}{e})

f (x) = \frac{1 - x}{9 + x}

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

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

f (x) = 8 x - 9 x^{(\frac{8}{9})}

f (x) = 33 x + 66 y + x y - x^{2} - 3 y^{2}

What is the extreme f(x)=3xe^{-x} ?
The extreme f(x)=3xe^{-x} is Maximum(1, 3/e)