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The Mean Value Theorem posits that during the trip, there was at least one moment where the vehicle's speed equaled the average speed of 90 km/h. This practical example underscores the theorem's significance in interpreting real-world scenarios, particularly in motion and velocity.
Conclusion
The Mean Value Theorem serves as a crucial mathematical tool that equates average and instantaneous rates of change, demonstrating the connection between a function’s behavior across an interval. Through its application in varied examples—from polynomial functions to real-life scenarios involving speed—the MVT showcases its relevance and utility in calculus. Understanding this theorem equips students and practitioners alike with a deeper insight into the dynamics of functions and rates of change.