I'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

I'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.