What is the extreme f(x)=9xe^{-x} ?

The extreme f(x)=9xe^{-x} is Maximum(1, 9/e)

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extreme f(x)=9xe^{-x}

extreme points

f (x) = 9 x e^{- x}

Maximum (1, \frac{9}{e})

Solution steps

Find the critical points:

x = 1

Domain of

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

9 x e^{- x} \Rightarrow y = \frac{9}{e}

Maximum (1, \frac{9}{e})

f (x) = - x^{3} + 12 x - 7

f (x) = x^{2} - 11, - 2 \leq x \leq 4

f (x) = 3 x^{3} - 36 x^{2} + 108 x + 8

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

f (x) = \frac{x}{2} - sin (x), - π \leq x \leq π

What is the extreme f(x)=9xe^{-x} ?
The extreme f(x)=9xe^{-x} is Maximum(1, 9/e)