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1 answer:
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First we have to find the derivative of the function:
f ` ( x ) = ( ln x / x^6 ) ` =
=
The critical point is when f ` ( x ) = 0
1 - 6 ln x = 0
6 ln x = 1
ln x = 1/6
![x = \sqrt[6]{e}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%5B6%5D%7Be%7D%20)
f ( e^(1/6)) = e^(-1) * 1/6 = 1 / (6 e)
Answer:
![( \sqrt[6]{e}; \frac{1}{6e} )](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5B6%5D%7Be%7D%3B%20%20%5Cfrac%7B1%7D%7B6e%7D%20%20%29)
f ` ( x ) = ( ln x / x^6 ) ` =
=
The critical point is when f ` ( x ) = 0
1 - 6 ln x = 0
6 ln x = 1
ln x = 1/6
f ( e^(1/6)) = e^(-1) * 1/6 = 1 / (6 e)
Answer: