Can i determine if a function will increase in the future? Is it possible to determine whether a function will have increased in the future relative to starting points, given a sample of the first $m$ points?
For example, given the 4 first values of a function $(f(1), f(2), f(3), f(4) )= (2, 1, 4, 5 )$ can I with some probability determine whether the $f(n)$ will be larger than all $f(1)$ to $f(4)$.
I apologize if this is too vague. Any answers appreciated
EDIT:
Thanks for commenting. If i let my function be something like a ratio of how many white and black marbles i have in my collection, and i keep adding marbles (non-fair with no known probability), can i then pursue something?

If there is a causal relation between the successive function values, you can hope for reliable extrapolation. For instance by linear prediction.
