Please explain why, label any formulas used, thanks!

2016 AP CALCULUS BC FREE-RESPONSE QUESTIONS 6. The function f has a Taylor series about x = 1 that converges to f(x) for all x in the interval of convergence. It is known that f(1) = 1, f'(1) = -7, and the nth derivative of f at x = 1 is given by f(") (1) = (1) (n -1)! 2n for n 2 2. (a) Write the first four nonzero terms and the general term of the Taylor series for f about x = 1. (b) The Taylor series for f about x = 1 has a radius of convergence of 2. Find the interval of convergence. Show the work that leads to your answer. (c) The Taylor series for f about x = 1 can be used to represent f(1.2) as an alternating series. Use the first three nonzero terms of the alternating series to approximate f(1.2). (d) Show that the approximation found in part (c) is within 0.001 of the exact value of f(1.2)