Which of the following statements are true ?

 

A) Rolle's theorem guarantees the existence of a c in the open interval (a, b) where the derivative of a function equals zero.

B) The Extreme Value Theorem states that a continuous function on a closed interval must achieve both a maximum and minimum value.

C) Rolle's theorem guarantees the existence of a c in the closed interval [a, b] where the derivative of a function equals zero

D) The Extreme Value Theorem states that the maximum and minimum value of a continuous function on an open interval (a, b) always exists and is equal.