Mean Value Theorem AP Calculus Ms. Olifer.

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Presentation transcript:

Mean Value Theorem AP Calculus Ms. Olifer

What you’ll learn about Mean Value Theorem Physical Interpretation Increasing and Decreasing Functions Other Consequences …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