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Using the Mean Value Theorem

Samuel Baker

Samuel Baker

6 min read

Study Guide Overview

This study guide covers the Mean Value Theorem (MVT). It explains the theorem, its conditions (continuity and differentiability), and its formula. It includes a walkthrough example and practice problems applying the MVT to find a point c where the instantaneous rate of change equals the average rate of change over a given interval. The guide also reviews the concepts of continuity and differentiability.

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Question 1 of 10

The Mean Value Theorem states that if a function ff is continuous on [a,b][a, b] and differentiable on (a,b)(a, b), then there exists a cc in (a,b)(a,b) such that which of the following is true?

f′(c)=f(b)−f(a)f'(c) = f(b) - f(a)

f′(c)=f(a)−f(b)b−af'(c) = \frac{f(a) - f(b)}{b - a}

f′(c)=f(b)−f(a)b−af'(c) = \frac{f(b) - f(a)}{b - a}

f′(c)=f(a)+f(b)b−af'(c) = \frac{f(a) + f(b)}{b - a}