Educator

Mean Value Theorem and Rolle's Theorem

• You should memorize the Mean Value Theorem and Rolle’s Theorem – including the continuity and differentiability hypotheses.
• If you are using one of these theorems, do check that the continuity and differentiability hypotheses are satisfied.
• If a problem asks you to verify a conclusion of one of these theorems, use algebra to do so.
• Note that Rolle’s Theorem is simply a special case of the Mean Value Theorem.