I’m a little confused on how Taylor series work, but from what I understand, they’re used to represent functions as an infinite sum of terms with its derivative—which I am deducting is only possible by the function being infinitely differentiable, correct? If that is the case, then why did my professor write a question asking for us to develop the Taylor series of f(x)=3x² 7x 1 at a=2 (that’s all the info he gives)? Furthermore, he says that f(x) is equal to 27 19(x-2) 3(x-2)² without indicating any approximation of error. So I’m confused on how a Taylor series can represent a function with a finite derivative and if my professor’s representation of his function is accurate without indicating an approximation of the error?