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Popular >

extreme f(x)=xe^{-x/2}

Solution

extreme points

f (x) = x e^{- \frac{x}{2}}

Solution

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

Solution steps

f^{'} (x) = e^{- \frac{x}{2}} (1 - \frac{x}{2})

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 2

into

x e^{- \frac{x}{2}} : \frac{2}{e}

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

Graph

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Frequently Asked Questions (FAQ)

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