(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

J(f)=[itex]\int[/itex] 2xf−f′^{2}+3f^{2}f′dx

f(0)=0,f(1)=−1.

2. Relevant equations

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

3. The attempt at a solution

F_{f}=2x+6f f''

F_{f'}=-2f' + 6f^{2}

Plugging in, I get:

2x+6f f''- [itex]\frac{d}{dx} (-2f' + 6f^{2})

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.

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# Homework Help: Extremum Function of a Functional

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