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hiii mate
This one is a courtesy of the book Calculus: Late Transcendentals, page 255.
You are driving on a straight highway on which the speed limit is 55 mi/h. At 8:05 A.M. a police car clocks your velocity at 50 mi/h and at 8:10 A.M. a second police car posted 5 miles down the road clocks your velocity at 55 mi/h. Explain why the police have a right to charge you with a speeding violation.
So why do the police have a right to hand you a speeding ticket?
Well, you traveled 5 miles in 5 minutes, or 112hr112hr. That’s equal to 60 mi/hr. Since your average velocity is 60 mi/hr, the Mean Value Theorem guarantees that your instantaneous velocity was 60 mi/hr at least once in the 5 mile stretch of highway.
What are the real life applications of the Mean Value Theorem?
In the context of kinematics, the Mean Value Theorem guarantees that an object’s instantaneous velocity was the average velocity at least once in a given time interval. That is, it guarantees that
dv/dt (t=c)=v(b)−v(a)/b−a
for at least one value of cc such that a<c<b
This one is a courtesy of the book Calculus: Late Transcendentals, page 255.
You are driving on a straight highway on which the speed limit is 55 mi/h. At 8:05 A.M. a police car clocks your velocity at 50 mi/h and at 8:10 A.M. a second police car posted 5 miles down the road clocks your velocity at 55 mi/h. Explain why the police have a right to charge you with a speeding violation.
So why do the police have a right to hand you a speeding ticket?
Well, you traveled 5 miles in 5 minutes, or 112hr112hr. That’s equal to 60 mi/hr. Since your average velocity is 60 mi/hr, the Mean Value Theorem guarantees that your instantaneous velocity was 60 mi/hr at least once in the 5 mile stretch of highway.
What are the real life applications of the Mean Value Theorem?
In the context of kinematics, the Mean Value Theorem guarantees that an object’s instantaneous velocity was the average velocity at least once in a given time interval. That is, it guarantees that
dv/dt (t=c)=v(b)−v(a)/b−a
for at least one value of cc such that a<c<b
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