Let f + ε ε η η be the result of such a perturbation ε ε η η of f , where ε ε is small and η η is a differentiable function satisfying η η ( a ) = η η ( b ) = 0 . Then define Φ Φ ( ε ε ) = J [ f + ε ε η η ] = ∫ ∫ a b L ( x , f ( x ) + ε ε η η ( x ) , f ′ ( x ) + ε ε η η ′ ( x ) ) d x .