No that way I could have chosen infinity at 10 or lower values also. f ' will go from 0 to 0 through positive values only. But how can I claim then that my solution is infinity independent. Because if I change the value of infinity whole solution changes.

Moreover at 15.6 the value of f ' is sufficiently close to 0 but value of g (0) is about 0.15 which is far greater than 0. g (0) goes to zero at about eta=25.

So  can I get rid of the problem?  

I tried to solve two coupled non-linear ordinary differential equations that arises in case of natural convection from an isothermal vertical flat plate. The problem is a boundary value one. The boundary conditions for the problem are at eta=0, f '(0)=0, f(0)=0, g(0)=1 and at eta=infinity f '(eta)=0, g(eta)=0. f ' should go from zero to zero through positive values but after a certain value of eta f ' is going to negative values until the value of eta =infinity at which it...