AP CALCULUS
ROLLE’S THEOREM/MEAN VALUE THEOREM
In problems 1 – 5, state whether or not the function satisfies the hypotheses of the Mean Value Theorem on the
given interval, and if it does find each value of c in the interval that satisfies the theorem.
1. 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 1 on [0,1]
2. 𝑓(𝑥) = 𝑥
2⁄
3
on [0,1]
3. 𝑓(𝑥) = 𝑥
1⁄
3
on [−1,1]
4. 𝑓(𝑥) = ln(𝑥 − 1) on [2,4]
5. 𝑓(𝑥) = |𝑥 − 1| on [0,4]
7.
8.
9.
10.
11.