Asked by Si
Find the x coordinate of the absolute maximum for the function f(x)= (2+6lnx) / x?
x>0
xcoordinate of abs max is?
x>0
xcoordinate of abs max is?
Answers
Answered by
Damon
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
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
Answered by
Si
I meant 2+6ln(x) divided by x. I don't know if that's what you were thinking or different?
Answered by
Damon
Yes
[ 2 + 6 ln x ] /x
= 2/x + (6/x) ln x
that makes it easy to take the derivative
[ 2 + 6 ln x ] /x
= 2/x + (6/x) ln x
that makes it easy to take the derivative
Answered by
Si
Hmm, I tried e but it wasn't right.
Answered by
Damon
zero when
2/x^2 +(6/x^2)lnx = 6/x^2
6 ln x = 4
ln x = 2/3
x = 1.95
2/x^2 +(6/x^2)lnx = 6/x^2
6 ln x = 4
ln x = 2/3
x = 1.95
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