Question: For any constant a, let f(x) = ax - x ln x for x > 0.
(a) What is the x-intercept of the graph of f(x)?
(b) Graph f(x) for a = -1 and a = 1.
(c) For what values of a does f(x) have a critical point for x > 0? Find the coordinates of the critical point and decide if it is a local maximum, a local minimum, or neither.