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Popular >

extreme xe^{-x}

Solution

extreme points

x e^{- x}

Solution

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

Solution steps

f^{'} (x) = e^{- x} (1 - x)

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 1

into

x e^{- x} : \frac{1}{e}

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

Popular Examples

intercepts of f(x)=(x^2-9)/(x+3)intercepts

f (x) = \frac{x ^{2} - 9}{x + 3}

inverse of f(x)=x^2-4x-3 inverse

f (x) = x^{2} - 4 x - 3

inverse of f(x)=sqrt(x+2)-7 inverse

f (x) = x + 2 - 7

perpendicular y=5x+2,(1,1)perpendicular

y = 5 x + 2, (1, 1)

asymptotes of f(x)=(3x-x^2)/(x^4-9x^2)asymptotes

f (x) = \frac{3 x - x ^{2}}{x ^{4} - 9 x ^{2}}

Frequently Asked Questions (FAQ)

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