One of the problems addressed by this chapter is this: suppose we know information about a function and its derivatives at a point, such as $$f(1) = 3\text{,}$$ $$\fp(1) = 1\text{,}$$ $$\fp'(1) = -2\text{,}$$ $$\fp''(1) = 7\text{,}$$ and so on. What can I say about $$f(x)$$ itself? Is there any reasonable approximation of the value of $$f(2)\text{?}$$ The topic of Taylor Series addresses this problem, and allows us to make excellent approximations of functions when limited knowledge of the function is available.