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The mean value theorem states that if F x is a differentiable function on the interval a b then there exists some number c between a and b such that the following formula is true Use this to explain why the mean value theorem implies that if a car averages 58 miles per hour in some 25 minute interval then the car s instantaneous velocity is 58 miles per hour at least once in that interval F c F b F a b a Choose the correct answer below OA The car s speed of 58 miles per hour is defined as the average rate of change of the car at point c or f c Since car drives continuously over a 25 minute interval or 0 25 the function is continuous Thus the mean value theorem can be applied OB The car s speed of 58 miles per hour is defined as the average rate of change of the car at point c making the function continuous Since the function is continuous it has a derivative at every point Thus the mean value theorem can be applied C The car s time of 25 miles per hour is defined as the average rate of change of the car at point c making the function continuous Since the function is continuous it has a derivative at every point Thus the mean value theorem can be applied OD The car s time of 25 miles per hour is defined as the average rate of change of the car at point c or f c Since the car drives continuously at an average speed of 58 miles per hour the function is continuous Thus the mean value theorem can be applied

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