I think the word you're looking for is extrapolate. It means (in one dimension) that you are given f(x) for various x in [a,b] and want to estimate f(x) for some x>b or some x<a.
Of course, you can use any method, and the accuracy you get depends on the situation. If I understand correctly, a cubic spline would end up being just a cubic function approximation, and so would assume the third derivative of the function is approximately constant. Your accuracy will depend on how well this actually fits the situation.
As an example, here
Taylor series - Wikipedia, the free encyclopedia
there is a graph of various polynomial approximations to the function . You can see that the cubic approximation is pretty good for but really gets bad as you go further from 0.