# Quiz 6

1. (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 $(a,b)$.
2. (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.