Question

g(x) = x^4lnx what are the critical points of g?

Answer 1

Use Product rule to find derivative

Answer 2

Find out where your derivative function hit zero

Answer 3

take log on both side.
log(y)=4ln(x)log(x)
(1/y)dy/dx=(4/x)log(x)+(4/x)log(x)
dy/dx=y[(8/x)log(x)]
x^4lnx[(8/x)log(x)]=0
from here we find either x=0 or x=1 but x cant be 0 because domain of log(x) is greater then 0.
so ans is 1