When ε ε = 0 , Φ Φ has an extremum value, so that d Φ Φ d ε ε | ε ε = 0 = ∫ ∫ a b [ η η ( x ) ∂ ∂ L ∂ ∂ f ( x , f ( x ) , f ′ ( x ) ) + η η ′ ( x ) ∂ ∂ L ∂ ∂ f ′ ( x , f ( x ) , f ′ ( x ) ) ] d x = 0 .