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Derivative Problem

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    I have to find the min and max of this function using derivatives:

    (e^(-x)) - (e^(-2x))




    3. The attempt at a solution
    f'(x) = -e^(-x) + 2x(e^(-2x))
    So now i set that to zero, and I get...

    2x(e^(-2x)) = e^(-x)

    And at this point I have no idea what to do. If you divide e^-x by e^-2x can u do something with the exponents?
     
  2. jcsd
  3. Apr 26, 2009 #2
    Double check your derivative, you shouldn't be bringing an x down right? The derivative of ecx for a constant c is just cecx
     
  4. Apr 26, 2009 #3
    o i ggot it! so it become

    2 = e^(-x-2x)
    and then you simply take the ln...

    thanks jeffreydk
     
  5. Apr 26, 2009 #4
    No problem.

    Watch out though, I think you have a sign error in there.

    f'(x)=-e-x+2e-2x=0

    So then 2e-2x=e-x

    and therefore by dividing you get 2=e-x+2x
     
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