Question

given the following function x>0, on which interval is the function decreasing? f(x)= x/ln(11x)

Answer 1

function is decreasing when f'(x) < 0
find f'(x) using quotient rule
\[f'(x) = \frac{\ln (11x) - 1}{\ln (11x)^{2}} \lt 0\]

Answer 2

how did you do that? and would i solve it like a regular equation, in order to get the coordinates for the answer?!

Answer 3

i took the derivative, have you learned derivatives yet?
otherwise you have to graph function to see where its decreasing

anyway like i said , f(x) is decreasing when f'(x) < 0
from there you have to solve for x
\[\frac{\ln (11x) -1}{\ln (11x)^{2}} < 0\]
\[\ln(11x) -1 < 0\]
\[\ln(11x) < 1\]
\[11x < e\]
\[x < \frac{e}{11}\]

Answer 4

Note: function not defined when ln(11x) = 0 --> x = 1/11
given x>0, the decreasing interval is
(0,1/11) U (1/11, e/11)