What is the extreme x2^{-x} ?

The extreme x2^{-x} is Maximum(1/(ln(2)), 1/(2^{\frac{1){ln(2)}}ln(2)})

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extreme x2^{-x}

extreme points

x 2^{- x}

Maximum (\frac{1}{ln ( 2 )}, \frac{1}{2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: \frac{1}{ln ( 2 )} < x < \infty

Plug

x = \frac{1}{ln ( 2 )}

into

x 2^{- x} : \frac{1}{2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )}

Maximum (\frac{1}{ln ( 2 )}, \frac{1}{2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )})

f (x) = 8 x^{3} + 2 x y - 3 x^{2} + y^{2} + 1

f (x) = \frac{( x + 1 )}{x ^{2}}

f (x, y) = 2 x^{2} + 16 y^{2} - 4 x y^{2}

f (x, y) = (x + 2 y)^{y}

f (x) = x^{4} - 16 x^{3}

What is the extreme x2^{-x} ?
The extreme x2^{-x} is Maximum(1/(ln(2)), 1/(2^{\frac{1){ln(2)}}ln(2)})