The term 'c in (a, b)' refers to a specific point within the open interval from a to b, where a and b are the endpoints. This point is significant in the context of calculus as it often represents a location where certain conditions, such as the equality of slopes or the existence of derivatives, hold true based on fundamental theorems. Understanding the role of c is crucial for analyzing how functions behave within that interval and can be vital for applying key results related to continuity and differentiability.
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