posted inside:)

thank you!! :D

Question

posted inside:) 

thank you!! :D

anonymous · Answer

Part 1: 

Find EXACT answer.

x=_________

please explain? :)

phi · Answer

they want you to find the maximum of some function of x
the standard way is
given f(x)
solve  f'(x) =0
which gives the critical points (min, max or an inflection point)
hopefully we will find a max for this problem

anonymous · Answer

okay:)

so where do we begin?

phi · Answer

$$ f(x)= x^{\frac{1}{x}} $$
find the derivative f'(x)

anonymous · Answer

f ' (x) = (1/x)*x^(1/x - 1) 
    =  $$(\frac{ 1 }{ x^2 })^{-1/x}$$

is that right? :/

anonymous · Answer

See http://www.youtube.com/watch?v=x6j9khJSArw

anonymous · Answer

oh so it should be this? since it's implicit? $$f'(x)=(x ^{-2+\frac{ 1 }{ x }})(1-\ln \left| x \right|)$$ ?

anonymous · Answer

what happens now?

anonymous · Answer

@phi ? @BillBell ?

phi · Answer

looks nice.  set = 0 and solve for x
the first part can never be 0, so it comes down to solving 1 - ln(x) =0
(remember x is assumed positive so we don't need the | | , not that it matters)

anonymous · Answer

ohh okay 

so 1-ln(x) = 0
   -ln(x) = -1 
     ln(x) = 1 
    x=0

? :/

phi · Answer

ln(x) = 1
make each side the exponent of e
$$ e^{\ln(x)} = e^1 $$

anonymous · Answer

ohh okay so x=e^1 ? 

x= 2.718281828 ?

phi · Answer

yes.  but I think they want x=e  (which is exact)

anonymous · Answer

ohh okay :)

awesome!! Thank you! :D

anonymous · Answer

ohh okay :)

awesome!! Thank you! :D