Topic
mean value theorem
on the existence of a tangent to an arc parallel to the line through its endpoints
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on the existence of a tangent to an arc parallel to the line through its endpoints
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In calculus and real analysis, the mean value theorem is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous rate of change at some point in the interval. For example, if a car smoothly travels a certain distance over a given finite time interval, then at some moment during the trip, its instantaneous speed equals its average speed for the whole trip.
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