Question

A relative maximum of the function f(x)=(lnx)^2/x occurs at...
Answer: e^2
Please show work and explain how to come to the answer.

Answer 1

take the derivative, set it equal to zero and solve

Answer 2

you got \(f'(x)\) ?

Answer 3

I tried to do that. Would it be easier to use the product rule or the quotient rule?

Answer 4

you have no choice, you have to use the quotient rule

Answer 5

ok I'll try that.

Answer 6

not too hard
\[\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}\] with
\[f(x)=(\ln(x))^2, f'(x)=\frac{2\ln(x)}{x},g(x)=x, g'(x)=1\]

Answer 7

Thanks I got it. :)