Question

Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined.
Find A
Find B
For each of the following intervals, tell whether f(x) is increasing or decreasing .
(A,B]:
[B,∞):

Answer 1

I will give you the derivative, you should be able to take it from there

f ' (x) = (x^6(1/x) - lnx(6x^5) )/x^12
= (x5 - 6x^5(lnx))/x^12

Answer 2

I know how to take the derivative the other parts i don't know how to do...

Answer 3

To figure out whether f(x) is increasing or decreasing, substitute any number from each of one of the intervals into f'(x). If you get a positive number for f'(x), then f(x) is increasing on that interval. If you get a negative number for f'(x), then f(x) is decreasing on that interval.