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Popular >

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

Solution

extreme points

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

Solution

Maximum (2, \frac{1}{e ^{2}})

Solution steps

f^{'} (x) = - e^{- x} (x - 2)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 2

into

(x - 1) e^{- x} : \frac{1}{e ^{2}}

Maximum (2, \frac{1}{e ^{2}})

Popular Examples

domain of 1/(sqrt(x+3))domain

\frac{1}{x + 3}

asymptotes of f(x)=((-2x^2))/(x^2+4x-5)asymptotes

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

inverse of f(x)= 7/8-x inverse

f (x) = \frac{7}{8} - x

extreme f(x)=-x^3+27x-52 extreme points

f (x) = - x^{3} + 27 x - 52

inverse of f(x)=(4x+10)/(2x-14)inverse

f (x) = \frac{4 x + 10}{2 x - 14}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x-1)e^{-x} ?
The extreme f(x)=(x-1)e^{-x} is Maximum(2, 1/(e^2))