Let F : ]0, +[infinity][ × R → R be the function F(x, y)=y(e**y +x)-ln(x).
Show: there exists a neighborhood I ⊂ R of the point x0 = 1 and a unique function f :I →R such that.
(1) f(1) = 0 and f ∈ C1(I),
(2) F(x, f(x)) = 0 for all x ∈ I.
( f ∈ C1(I), means that f is differentiable and that the derivative is continuous. )
