Essential Understanding 2.4

Essential Understanding 2.4 Students will understand that the Mean Value Theorem connects the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval.

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Learning Objective 2.4A Students will be able to apply the Mean Value Theorem to describe the behavior of a function over an interval.

Essential Knowledge 2.4A1 Students will know that if a function f is continuous over the interval [a, b] and differentiable over the interval (a, b), the Mean Value Theorem guarantees a point within that open interval where the instantaneous rate of change equals the average rate of change over the interval.