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Popular >

extreme f(x)=xe^{-x/3}

Solution

extreme points

f (x) = x e^{- \frac{x}{3}}

Solution

Maximum (3, \frac{3}{e})

Solution steps

f^{'} (x) = e^{- \frac{x}{3}} (1 - \frac{x}{3})

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 3

into

x e^{- \frac{x}{3}} : \frac{3}{e}

Maximum (3, \frac{3}{e})

Graph

Popular Examples

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

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f (x) = 2 x^{3} - 36 x^{2} + 210 x - 15

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\frac{x}{x ^{2} + 16}

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f (x) = - 4 cos (3 x) - 4

Frequently Asked Questions (FAQ)

What is the extreme f(x)=xe^{-x/3} ?
The extreme f(x)=xe^{-x/3} is Maximum(3, 3/e)