(Problem 2, continued) B. [10 pts] Morgan, Avery, and Taylor are asked to compute f(1)(1) and provide the following argument. We know that all f(11) (1) 11! , so 11! . an = f()(1). Also, an is the coefficient of (x - 1) . Since (ac - 1)3k = (x - 1)" when 3k = 11, we see that k = 11/3. Unfortunately, they cannot agree on how to interpret the result. 3. (-1)k . 2k 3 . (-1)11/3 . 211/3 9 . 211/3 . Morgan claims that since k = 11/3, an1 = = k+1 Ik=11/3 14/3 14 9 . 211/3 Hence, Morgan believes that f(1D) (1) = 11! . an = 11!. 14 . Avery notes that k = 11/3 is not an integer, so f()(1) does not exist. . Taylor notes that k = 11/3 is not an integer, so f(1) (1) = 0. Explain which, if any of the students is correct. Make sure to justify your answer via an explanation and/ or a calculation. Do not simply quote a result that may have been discussed in lecture or recitation