What is the extreme f(x)=(5-x)5^x ?

The extreme f(x)=(5-x)5^x is Maximum(-1/(ln(5))+5,(5^{\frac{-1+5ln(5))/(ln(5))}}{ln(5)})

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extreme f(x)=(5-x)5^x

extreme

Maximum (- \frac{1}{ln ( 5 )} + 5, \frac{5 ^{\frac{- 1 + 5 l n ( 5 )}{l n ( 5 )}}}{ln ( 5 )})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = - \frac{1}{ln ( 5 )} + 5

into

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

Maximum (- \frac{1}{ln ( 5 )} + 5, \frac{5 ^{\frac{- 1 + 5 l n ( 5 )}{l n ( 5 )}}}{ln ( 5 )})

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