Question

Find the x coordinate of the absolute maximum for the function f(x)= (2+6lnx) / x?

x>0

xcoordinate of abs max is?

Answer 1

y = 2/x + (6/x) ln x
dy/dx = -2/x^2 +(6/x)(1/x) + ln x (-6/x^2)

zero when
2/x^2 +(6/x^2)lnx = 6/x^2

3 ln x = 3
ln x = 1
x = e

Answer 2

I meant 2+6ln(x) divided by x. I don't know if that's what you were thinking or different?

Answer 3

Yes

[ 2 + 6 ln x ] /x

= 2/x + (6/x) ln x

that makes it easy to take the derivative

Answer 4

Hmm, I tried e but it wasn't right.

Answer 5

zero when
2/x^2 +(6/x^2)lnx = 6/x^2

6 ln x = 4

ln x = 2/3
x = 1.95