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Mean Value Theorem

Applying the first derivative test and mean value theorem.

Mapped to AP College Board # FUN-1, FUN-1.B, FUN-1.B.1

Existence theorems allow us to draw conclusions about a function’s behavior on an interval without precisely locating that behavior. Justify conclusions about functions by applying the Mean Value Theorem over an interval. If a function f is continuous over the interval [a, b] and differentiable over the interval (a, b), then 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.