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 2 years ago
Find the critical numbers of the function. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.)
f(x) = x^−6 ln x
 2 years ago
Find the critical numbers of the function. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.) f(x) = x^−6 ln x

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Jusaquikie
 2 years ago
Best ResponseYou've already chosen the best response.0the actual question is \[x^{6}\ln x\] I think the derivative is \[x^{7}6x^{7}\ln x \]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1derivative is better written as \[\frac{16\ln(x)}{x^7}\] makes finding the critical points a lot easier

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1on critical point is 0, but that is not in the domain of your function. so you can ignore it other one solve \[16\ln(x)=0\]

Jusaquikie
 2 years ago
Best ResponseYou've already chosen the best response.0i think part of my problem is i don't know how to solve for ln

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[16\ln(x)=0\] \[6\ln(x)=1\] \[\ln(x)=\frac{1}{6}\] \[x=e^{\frac{1}{6}}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1like that you are going to have to "exponentiate" at some point

Jusaquikie
 2 years ago
Best ResponseYou've already chosen the best response.0ok thanks, i know eulers number is related to natural log i just don't know how to convert back and forth. thanks for the help

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\ln(x)=y\iff e^y=x\]

Jusaquikie
 2 years ago
Best ResponseYou've already chosen the best response.0so if i had ln23 that would be e^23?

Jusaquikie
 2 years ago
Best ResponseYou've already chosen the best response.0actually ln23 is 3.13 so E^3.13 = 23?
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