Sergio Sanchez - Network Science

Given a function f(x), it is known that its first derivative is f'(x) = 3x^2 - 12x + 9. What can be said about the behavior of f(x)? A. The function has a maximum at x = 1. B. The function has a minimum at x = 3. C. The function is increasing for x > 3 and decreasing for x < 1. D. The function is increasing in the intervals (-∞, 1) and (3, ∞), and decreasing in the interval (1, 3). E. None of the above. Original idea by: Sergio Sanchez

Consider the following statements: A. Given a tree T, it is possible to find the diameter of T using two BFS executions. B. If an undirected graph is bipartite, it can be detected using BFS. C. BFS was run on a connected simple graph, starting from a node r. Let u and v be two nodes in the graph. If the distance from r to u is 2, and the distance from r to v is 1, then the distance between u and v in the graph must necessarily be 1. Which of the statements are correct? a) Only A b) Only B c) A and B d) B and C e) None of the above