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Popular >

extreme y=x+e^{-4x}

Solution

extreme points

y = x + e^{- 4 x}

Solution

Minimum (\frac{ln ( 2 )}{2}, \frac{ln ( 2 )}{2} + \frac{1}{4})

Solution steps

f^{'} (x) = 1 - 4 e^{- 4 x}

Find intervals:

Decreasing

: - \infty < x < \frac{ln ( 2 )}{2},

Increasing

: \frac{ln ( 2 )}{2} < x < \infty

Plug

x = \frac{ln ( 2 )}{2}

into

x + e^{- 4 x} : \frac{ln ( 2 )}{2} + \frac{1}{4}

Minimum (\frac{ln ( 2 )}{2}, \frac{ln ( 2 )}{2} + \frac{1}{4})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme y=x+e^{-4x} ?
The extreme y=x+e^{-4x} is Minimum((ln(2))/2 ,(ln(2))/2+1/4)