Assignment:
Consider the function f(x) = 4kx^(3) - (k^2 - 13)x + 9k, where k is a constant.
(a) Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.
(b) If f has a relative maximum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.
(c) If f has a relative minimum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.
Provide complete and step by step solution for the question and show calculations and use formulas.