### Finding the Critical Point and Relative Minimum and Maximum

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. Answer: f has a critical point at x = 1 exactly when k = ______ (b) If f has a relative max