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How do you solve this equation (involving exponentials)?

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    0=x(e^-x)

    2. Relevant equations



    3. The attempt at a solution

    Well as x is a multiple that leaves:
    0=e^-x
    so does x=0?

    Any help at all would be greatly appreciated. Many Thanks.
     
    Last edited: Oct 21, 2009
  2. jcsd
  3. Oct 21, 2009 #2

    Mark44

    Staff: Mentor

    If a*b = 0 then a = 0 or b = 0.
    For your equation, either x = 0 or e-x = 0.
    Clearly, x = 0 is a solution of your equation. Are there any values of x for which e-x = 0?
     
  4. Oct 21, 2009 #3
    Well wouldn't x be infinity in that case?
    But this question is referring to co-ordinates of a turning point so surely a turning point cant be infinity?

    The original equation was y=(x^2)(e^-x)
    Which I differentiated into:
    dy/dx=x^2(-e^-x)+(e^-x)2x
    Which I factorised into:
    dy/dx=x(e^-x)[-x+2]

    And as dy/dx=0 for turning points then:
    0=x(e^-x)[-x+2]
    So x=2 and 0=x(e^-x)

    Is this all right?

    Thankyou so much.
     
  5. Oct 21, 2009 #4

    Mark44

    Staff: Mentor

    So x = 2 or x = ?
     
  6. Oct 21, 2009 #5
    Is it zero?
     
  7. Oct 21, 2009 #6

    Mark44

    Staff: Mentor

    Yes.
     
  8. Oct 21, 2009 #7
    Thankyou!
     
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