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A plane begins its takeoff at 2:00 pm on a 2500-mile flight. The plane arrives at its destination at 7:30 pm. Use the Mean Value Theorem to show that there were at least two times during the flight when the speed of the plane was exactly 400 mi/hr.

A plane begins its takeoff at 2:00 pm on a 2500-mile flight. The plane arrives at its destination at 7:30 pm. Use the Mean Value Theorem to show that there were at least two times during the flight when the speed of the plane was exactly 400 mi/hr.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 4: Mean Value Theorem Application** A plane begins its takeoff at 2:00 pm on a 2500-mile flight. The plane arrives at its destination at 7:30 pm. Use the Mean Value Theorem to show that there were at least two times during the flight when the speed of the plane was exactly 400 mi/hr. **Explanation**: This problem challenges us to apply the Mean Value Theorem from calculus to real-world situations, specifically in determining moments during a flight when a certain speed is achieved. The Mean Value Theorem states that for a continuous and differentiable function, there exists at least one point where the instantaneous rate of change (i.e., the derivative) is equal to the average rate of change over an interval. Here, this translates to finding at least two instances when the plane's speed reached exactly 400 miles per hour during its journey.
Transcribed Image Text:**Problem 4: Mean Value Theorem Application** A plane begins its takeoff at 2:00 pm on a 2500-mile flight. The plane arrives at its destination at 7:30 pm. Use the Mean Value Theorem to show that there were at least two times during the flight when the speed of the plane was exactly 400 mi/hr. **Explanation**: This problem challenges us to apply the Mean Value Theorem from calculus to real-world situations, specifically in determining moments during a flight when a certain speed is achieved. The Mean Value Theorem states that for a continuous and differentiable function, there exists at least one point where the instantaneous rate of change (i.e., the derivative) is equal to the average rate of change over an interval. Here, this translates to finding at least two instances when the plane's speed reached exactly 400 miles per hour during its journey.
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