Chapter 5 Applications of Derivatives Section 5.2 Mean Value Theorem.

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Presentation transcript:

Chapter 5 Applications of Derivatives Section 5.2 Mean Value Theorem

Quick Review

Quick Review Solutions

What you’ll learn about The Mean Value Theorem Increasing and decreasing functions Functions whose derivative is zero Antidifferentiation …and why The Mean Value Theorem is an important theoretical tool to connect the average and instantaneous rates of change.

Mean Value Theorem for Derivatives

Example Explore the Mean Value Theorem

Increasing Function, Decreasing Function

Corollary: Increasing and Decreasing Functions

Example Determining Where Graphs Rise or Fall

Corollary: Functions with f ′ = 0 are Constant

Corollary: Functions with the Same Derivative Differ by a Constant

Antiderivative

Example Finding Velocity and Position

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