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But the problem is that the definitions of those derivatives are for infonitesimal change. What about far away points?
by objektif 7y ago
But the problem is that the definitions of those derivatives are for infonitesimal change. What about far away points?
- AstralStorm 7y agoThe definition works for any point. However often for higher functions you need to break the function into ranges to find closed form derivative series and get a useful result.
- ddxxdd 7y agoFar away points have properties resembling infinitesimally close points, as long as the function is continuous. Now when there's a lack of continuity, then we run into a problem.
- galaxyLogic 7y agoI'm not a mathematician but I assume there are functions with infinite number of derivatives. For such you cannot know all the values of the function by knowing the values of all derivatives because you would have to know infinitely many numbers. Whereas if there are a fixed number of derivatives then at some level the derivative is constant and thus you can intuitively think that based on those derivatives you can then "draw" the function.
- jonsen 7y agoIn-phony-tesimal, I like that word.