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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = \frac{1}{2}

into

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

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

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Frequently Asked Questions (FAQ)

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