Finding Stationary Points for the Differential Equation y=(lnx)^2/x

[chwala]

Homework Statement

Get the two stationary points for the equation $y= ((ln x)^2)/x$

Homework Equations

The Attempt at a Solution

i have managed to solve
$dy/dx=((2xlnx/x- (ln x)^2))/x^2 = 0, ln x(2-ln x) = 0, x= 1, x =e^2$

 

[Astik]

therefore
dy/dx=2u/u=2dy/dx=2u/u=2dy/dx=2u/u = 2 is this correct?

I think you are trying to say here, dy/du = 2v/u and it's not equal to 2.

 

[BvU]

I can follow $$
{ dy\over dx} ={2x\ln x/x- (ln x)^2)\over x^2} = 0 \ \ \Leftrightarrow\ \ \ln x(2-ln x) = 0 \ \ \& \ \ x\ne 0 $$
which is satisfied for $x= 1$ and for $x =e^2$.
But the 'then I am getting' seems a bit superfluous to me. What do you intend to show with that ?

 

[Ray Vickson]

Homework Statement

Get the two stationary points for the equation $y= ((ln x)^2)/x$

Homework Equations

The Attempt at a Solution

i have managed to solve
$dy/dx=((2xlnx/x- (ln x)^2))/x^2 = 0, ln x(2-ln x) = 0, x= 1, x =e^2$

So, what is your question?

Anyway, please use proper syntax for TeX/LaTex: you should type "\ln ..." instead of "ln ...", because leaving out the backslash produces ugly results that are hard to read, like this ($ln x$) while using "\ln..." produces good-looking, easier-to-read results, like this ($\ln x$). BTW: the same goes for sin/arcsin, cos/arccos, tan/arctan, exp, log, max, min, lim, sinh, cosh, tanh, etc: leaving out the backslash gives ugly, hard-to-read results $sin x$, $arcsin x$, $cos x$, $arccos x$, $tan x$, $arctan x$, $exp x$, $log x$, $max x$, $min x$, $lim_{x \to 0}$, $sinh x$, etc., etc. Using the backslash produces much nicer output: $\sin x$, $\arcsin x$, $\cos x$, $\arccos x$, $\tan x$, $\arctan x$, $\exp x$, $\log x$, $\max x$, $\min x$, $\lim_{x \to 0}$, $\sinh x$, etc.

 

[chwala]

I a m sorry the question was to find the co ordinates of the stationary point for the given function $y= f(x)$

 

[BvU]

That is the problem statement. What Ray means is: what question do you want your helpers to answer ?

 

[chwala]

I have answered the question already sorry