Which of the following statements are true regarding the properties of continuous functions?
A) A continuous function on a closed interval must attain its maximum and minimum values (Weierstrass Theorem).
B) The continuity of a function at a point implies that the function is differentiable at that point.
C) The function f(x) = 1/x is continuous at x = 0.
D) The Intermediate Value Theorem guarantees that a continuous function that takes values of opposite signs at the endpoints of an interval must have at least one root in between.