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Extremum Function of a Functional

  1. Nov 13, 2011 #1
    1. The problem statement, all variables and given/known data

    J(f)=[itex]\int[/itex] 2xf−f′2+3f2f′dx
    f(0)=0,f(1)=−1.

    2. Relevant equations

    Ff-[itex]\frac{d}{dx}[/itex]Ff'=0

    3. The attempt at a solution

    Ff=2x+6f f''
    Ff'=-2f' + 6f2

    Plugging in, I get:
    2x+6f f''- [itex]\frac{d}{dx} (-2f' + 6f2)

    2x+6f f''-12f f'-2f''=0

    Which doesn't look correct to me.
    I'm guessing my mistake was in the differentiation, but I don't see it.
     
  2. jcsd
  3. Nov 14, 2011 #2
    I figured it out, algebra errors.
     
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