Calculus I (MATH 101) Rolle's Theorem and the Mean Value Theorem Exam Review
University of California, Berkeley
Calculus I (MATH 101) | Exam Review

Overview
An exam review that connects Rolle's theorem and the Mean Value Theorem to typical proof and application questions in Calculus I.

Key topics
•Rolle conditions and conclusion
•Mean Value Theorem statement
•checking continuity and differentiability
•finding the c value on an interval
•interpreting average vs instantaneous rate

Suggested study tasks
•verify conditions on 3 functions and intervals
•find c that satisfies MVT for a polynomial
•explain in words what the theorem guarantees
•spot a counterexample when conditions fail
•write a clean conclusion sentence referencing c in (a,b)

Common pitfalls
•forgetting to check endpoints for continuity
•assuming differentiability at a cusp or vertical tangent
•solving for c but not stating the interval
•mixing average rate with derivative at a point
•using the theorem when a function is not continuous