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''- \frac{d}{dx} (-2f&#039; + 6f²)<br /> <br /> 2x+6f f&#039;&#039;-12f f&#039;-2f&#039;&#039;=0<br /> <br /> Which doesn&#039;t look correct to me.<br /> I&#039;m guessing my mistake was in the differentiation, but I don&#039;t see it.

 

[Shantih]

I figured it out, algebra errors.