EXAMPLE 4 If an object moves in a straight line with position function s= f(t), then the average velocity between t=a and t= b is f(b)-f(a) b-a and the velocity at t-c is f'(c). Thus the Mean Value Theorem tells us that at some time tc between a and b the instantaneous velocity (c) is equal to the average velocity. For instance, if a car traveled 190 km in 2 hours, then the speedometer must have read X km/h at least once. In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval.

EXAMPLE 4 If an object moves in a straight line with position function s= f(t), then the average velocity between t=a and t= b is f(b)-f(a) b-a and the velocity at t-c is f'(c). Thus the Mean Value Theorem tells us that at some time tc between a and b the instantaneous velocity (c) is equal to the average velocity. For instance, if a car traveled 190 km in 2 hours, then the speedometer must have read X km/h at least once. In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 7CR

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