In the context of the Mean Value Theorem, 'c in (a, b)' refers to a specific point within the open interval (a, b) where the instantaneous rate of change of a function equals the average rate of change over that interval. This concept is crucial because it establishes that if a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one point 'c' where the tangent line to the curve is parallel to the secant line connecting points a and b. It connects the behavior of a function's derivative with its overall change across an interval.
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