Which of the following statements are true about continuous functions on a closed interval?
A) A continuous function on a closed interval [a, b] must be bounded.
B) A continuous function on a closed interval [a, b] must be differentiable.
C) The Intermediate Value Theorem applies to continuous functions on any interval, whether open or closed.
D) A function that is continuous at every point in an interval must be continuous on the entire interval.