Comments:

- (Section F): There are two basic assumptions in both Rolle’s theorem and the mean value theorem, which require the function f to be (1) continuous on the closed interval [a,b] and (2) differentiable on the open interval (a,b).
- (Section G): The extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once. Do not confuse it with other theorems.