Which of the following statements about the Intermediate Value Theorem and a function f(x) on the interval
(a,
b) are true? Select all that apply. If the conditions are true, there exists a value c in the interval
(a,
b) such that f
(c) = N. The options are:

A) The Intermediate Value Theorem guarantees the existence of a value c in the interval
(a,
b) such that f
(c) = N.
B) The Intermediate Value Theorem guarantees the existence of a value c in the interval
(a,
b) such that f
(c) = N, only if f(x) is continuous on the interval
(a,
b).
C) The Intermediate Value Theorem guarantees the existence of a value c in the interval
(a,
b) such that f
(c) = N, regardless of the continuity of f(x) on the interval
(a,
b).
D) The Intermediate Value Theorem guarantees the existence of a value c in the interval
(a,
b) such that f
(c) = N, only if f(x) is differentiable on the interval
(a,
b).