Determining an Exterior Normal Given a surface , that can be represented by the equation: $F(x,y,z)=0 $ . 
How can I determine which of the vectors $ -\text{gradF} ,\text {grad} F$ is the exterior normal and which is the interior normal?
In addition, if this surface can be represented as $ z=f(x,y) $ , we know that the vectors $ (f_x,f_y , -1 ) $ are normals. But how can I determine who is the exterior normal and who is the interior one?
Thanks ! 
 A: Let's assume, as Edgar Matias suggested, that our surface is compact, so we have the interior as the bounded region and the exterior as the unbounded one. I don't think that you can answer  this question by considering the gradient locally, since it's not too hard imagine two manifolds with the same gradient at a point, but where in one case the gradient is inward, and in the other case the gradient is outward (imagine a shape that folds over itself). 
One possible way of answering this question is to integrate the gradient over the manifold, fixing the outward orientation on the manifold. If the integral is positive, the gradient was the external normal, otherwise it was the internal normal.
A: For future reference I would like to propose a different method of checking this which may be simpler in practice. As Edgar Matias suggested, we need to assume that the surface is compact, so that there is an interior and exterior of the surface. For my method (and I think also for Elchanan Solomon's one) we also need to asssume that $\textrm{grad} F$ never vanishes on the surface, so that it doesn't change between pointing inwards and outwards.
Then, either $F$ is negative in the interior and positive in the exterior or the reverse. In both cases, the gradient will point towards the positive region, as the gradient points in the direction of maximum increase of $F$. We can check in which case we are in by simply evaluating $F$ close to infinity, as we know that "infinity" will be in the exterior. Formally, you just need to show that there are points with modulus arbitrary big where $F$ is positive/negative.
