Q: Given that G(x,y,z)=(6xz+x3, 3x2y+y2, 4x+2yz-3z2). Find F such that curl F = G. Solution: ... A particular solution is Fo=(-3x2yz-y2z, 2x2-3xz3-x3z) And then my textbook says that the general solution is F=Fo + grad f where f is an arbitrary C1 function. =============================== Now my questions: If f is C1 function, why must F=Fo+gradf be a solution to curl F=G? I believe that curl(grad f)=0 for f a C2 (not C1) function. Why does C1 work as well? Secondly, why can we be sure that F=Fo+gradf is the general solution to curl F=G? (i.e. why is every solution contained in it?) I would really appreciate if someone could explain.