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

1. Jusaquikie

the actual question is $x^{-6}\ln x$ I think the derivative is $x^{-7}-6x^{-7}\ln x$

2. satellite73

derivative is better written as $\frac{1-6\ln(x)}{x^7}$ makes finding the critical points a lot easier

3. satellite73

on critical point is 0, but that is not in the domain of your function. so you can ignore it other one solve $1-6\ln(x)=0$

4. Jusaquikie

i think part of my problem is i don't know how to solve for ln

5. satellite73

$1-6\ln(x)=0$ $6\ln(x)=1$ $\ln(x)=\frac{1}{6}$ $x=e^{\frac{1}{6}}$

6. satellite73

like that you are going to have to "exponentiate" at some point

7. Jusaquikie

ok 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

8. satellite73

$\ln(x)=y\iff e^y=x$

9. Jusaquikie

so if i had ln23 that would be e^23?

10. Jusaquikie

actually ln23 is 3.13 so E^3.13 = 23?