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

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

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

extreme points

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

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

Solution steps

Find the critical points:

x = 1

Domain of

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

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

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

F (x, y) = x^{6} - 3 x^{2} y^{2} + 3 x y^{3}

f (x) = (x^{2} + 7) (49 + x^{2})

f (x) = x^{4} - 6 x^{2} + 8 x

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{4} - 5 x + 5

f (x) = 6 x^{3} + x^{2} - 2

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