What is the extreme x(2^{-5x}) ?

The extreme x(2^{-5x}) is Maximum(1/(5ln(2)), 1/(5*2^{\frac{1){ln(2)}}ln(2)})

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extreme x(2^{-5x})

extreme

Maximum (\frac{1}{5 ln ( 2 )}, \frac{1}{5 \cdot 2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )})

Solution steps

f^{'} (x) = 3 2^{- x} (- 5 ln (2) x + 1)

Find intervals:

Increasing

: - \infty < x < \frac{1}{5 ln ( 2 )},

Decreasing

: \frac{1}{5 ln ( 2 )} < x < \infty

Plug

x = \frac{1}{5 ln ( 2 )}

into

x 2^{- 5 x} : \frac{1}{5 \cdot 2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )}

Maximum (\frac{1}{5 ln ( 2 )}, \frac{1}{5 \cdot 2 ^{\frac{1}{l n ( 2 )}} ln ( 2 )})

What is the extreme x(2^{-5x}) ?
The extreme x(2^{-5x}) is Maximum(1/(5ln(2)), 1/(5*2^{\frac{1){ln(2)}}ln(2)})