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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 fb) - {(а) b - а and the velocity at t = c is f'(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f'(c) is equal to the average velocity. For instance, if a car traveled 500 km in 5 hours, then the X km/h at least once. speedometer must have read 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 fb) - {(а) b - а and the velocity at t = c is f'(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f'(c) is equal to the average velocity. For instance, if a car traveled 500 km in 5 hours, then the X km/h at least once. speedometer must have read 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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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 fb) - {(а) b - а and the velocity at t = c is f'(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f'(c) is equal to the average velocity. For instance, if a car traveled 500 km in 5 hours, then the X km/h at least once. speedometer must have read 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.
Transcribed Image Text: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 fb) - {(а) b - а and the velocity at t = c is f'(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f'(c) is equal to the average velocity. For instance, if a car traveled 500 km in 5 hours, then the X km/h at least once. speedometer must have read 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.
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