Hi, I would really appreciate it if someone can help me with the following problem, regarding a taylor polynomial: A 2nd degree taylor polynomial to the function f around x = 1, is given by: T_2(x) = x + x^2 Question: What is f´(1) ? Answer: 3 (Btw: the question is from a multiple choice test, but the answer should be evident without consulting the possible answers) 2. Relevant equations I usually solve this kind of problem simply by considering the general form of a taylorpolynomial: f(a) + f´(a)(x-a) + (f´´(a)/2!) * (x-a)^2 and comparing it to the taylor polynomial given in the problem statement. From a little rearrangement, the answer is usually self-evident. But in this case the rearranging seems very elaborate, so im hoping that im missing some clever way to solve it. 3. The attempt at a solution In this case I really dont know how go about it. I´ve only managed to simply make sense of the answer, by the following argument: f(1) + f´(1)(x-1) + f´´(1)(x-1)]^2 = x + x^2 ⇔ f(1) + f´(1)x - f´(1) + f´´(1)(x^2 + 1 - 2x) = x + x^2 ⇔ f(1) + f´(1)x - f´(1) + f´´(1)x^2 + f´´(1) - f´´(1)2x = x + x^2 Inserting f´(1) = 3 evaluates to x + x^2 , if f´´(1) = 2 and f(1) = 2 . But there´s no way that I would have seen that, not knowing that f´(1) = 3 . There must be some nice way of solving this problem? Any help would be truly appreciated..!