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Help with Y'=0 wanted

  1. Aug 30, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm gonna solve the equation Y'=0 if Y=x*e-0,4x


    2. Relevant equations



    3. The attempt at a solution

    I can come as far as to Y'=(1-0,4x)*e-0,4x

    Where do I go from here?
    Can i just write (1-0,4x)*e-0,4x=0 ?

    I can solve the easier kinds of these equations, but this one is the hardest of the ones that I have, and I suspect that something like this will show up on a test in the future, so it would be good if I can solve it.

    Anyone can help me in the right direction?
     
  2. jcsd
  3. Aug 30, 2012 #2
    Since [tex]{e^a}[/tex] is always > 0 for every value of a, then assume your computed y' is correct, you only need to solve the equation: 1-0.4x = 0, as simple as that.
     
  4. Aug 30, 2012 #3

    Mark44

    Staff: Mentor

    Yes. Now, either 1 - 0.4x = 0 or e-.4x = 0.

    Note that e-.4x ≠ 0 for any real x.

    Edit: Didn't notice that drawar said essentially the same thing.
     
  5. Aug 30, 2012 #4
    So I only have to solve 1-0,4x=0 and that will be the whole answer for the whole equation?
     
  6. Aug 30, 2012 #5

    CAF123

    User Avatar
    Gold Member

    Well, the solution to 1-0.4x =0 solves Y'=0.
     
  7. Aug 30, 2012 #6
    I don't understand the whole thing :confused:

    Can somebody show all steps to solving this one?
    I really need to learn it.
     
  8. Aug 30, 2012 #7

    Mark44

    Staff: Mentor

    No, we won't do your work for you, but we'll help you do it.
    The problem, apparently, is to find the x value(s) for which f'(x) = 0, where f(x) = xe-.4x. (Changed from your notation of y(x) to f(x).)

    You found f'(x) = (1 - 0.4x)e-.4x

    If f'(x) = 0, then (1 - 0.4x)e-.4x.

    For what x is f'(x) = 0?
     
  9. Aug 30, 2012 #8
    According to some earlier posts the solution to 1-0.4x =0 solves Y'=0

    If x is 2.5 then it will be 0.

    But what should I do with e-0,4x?
     
  10. Aug 30, 2012 #9

    Mark44

    Staff: Mentor

    Nothing. As already mentioned, e-0.4x > 0 for all real x.
     
  11. Aug 30, 2012 #10
    Okay, so the answer to the problem is:
    y=x*e-0,4x
    y'=(1-0,4x)*e-0,4x

    y'=(1-0,4x=0
    x=2.5

    e-0,4x is always >0

    And this classifies as the correct answer?
     
  12. Aug 30, 2012 #11

    Mark44

    Staff: Mentor

    You have a lot of cruft in there that is unnecessary. Here is all you need to say:

    If y = x*e-0.4x, then y' = 0 when x = 2.5.
     
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