Extremum Function of a Functional

[Shantih]

Homework Statement

J(f)=$\int$ 2xf−f′²+3f²f′dx
f(0)=0,f(1)=−1.

Homework Equations

F_f-$\frac{d}{dx}$F_f'=0

The Attempt at a Solution

F_f=2x+6f f''
F_f'=-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.

 

[Shantih]

I figured it out, algebra errors.