Question

find critical numbers of the function f(x)=(x^-5)(lnx)

Answer 1

You need to use product rule to find f'(x) since you have a product for f

Answer 2

so f'(x)= (x^-5)(e^x)+(lnx)(-5x^-6)

Answer 3

derivative of ln(x) w.r.t x is 1/x

Answer 4

\[f'(x)=x^{-5} \frac{1}{x}+\ln(x)(-5x^{-6}) \\ f'(x)=x^{-6}+\ln(x)(-5x^{-6})\]
You can factor f'

Answer 5

then i just that equal to zero to find the critical values?

Answer 6

yep

Answer 7

thanks for the help i had a brain fart for a moment and forgot the log rules