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AP Calculus AB/BC
Unit 5 – Analytical Applications of Differentiation
Topic 5.1
What does the Mean Value Theorem state?
For any continuous function on a closed interval, there exists a value c in the interval such that the value of the function at c is equal to the average rate of change of the function over the interval.
For any differentiable function on an open interval, there exists a value c in the interval such that the value of the derivative of the function at c is equal to the average rate of change of the function over the interval.
For any function that is continuous on a closed interval, there exists a value c in the interval such that the value of the derivative of the function at c is equal to the average rate of change of the function over the interval.
For any function that is continuous on the closed interval and differentiable on the open interval, there exists a value c in the open interval such that the value of the derivative of the function at c is equal to the average rate of change of the function over the interval.
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AP Calculus AB/BC - 5.1 Using the Mean Value Theorem
Key terms
Mean Value Theorem
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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
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