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Math Help - mean value theorem

  1. #1
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    mean value theorem

    can you guys give me an example where this theorem would be used in the real world? Im trying to explain it to my friend but im having little luck with it since he's not a big math fan.

    thanks a lot
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  2. #2
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    Quote Originally Posted by nertil1 View Post
    can you guys give me an example where this theorem would be used in the real world? Im trying to explain it to my friend but im having little luck with it since he's not a big math fan.

    thanks a lot
    Let s(t) be your distance from your starting point at any time t\geq 0. You know that s'(t_0) is the velocity at that point. And \frac{s(t_2)-s(t_1)}{t_2-t_1} is the average (mean) velocity.
    Therefore we must have the mean velocity equal to the instatensous velocity at some point during the travel.
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  3. #3
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    Quote Originally Posted by nertil1 View Post
    can you guys give me an example where this theorem would be used in the real world? Im trying to explain it to my friend but im having little luck with it since he's not a big math fan.

    thanks a lot
    To prove someone had been speeding even though the speed of their vehicle
    when passing the check points was less than the speed limit. Since if the
    average speed between the check points d/t (where d is the distance
    between the check points and t the difference in the times of passing the
    check points) is greater than the speed limit then by the mean value theorem
    the vehicles instantaneous speed was greater than the speed limit at some
    point between the check points.

    RonL
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  4. #4
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    I must say the Mean Value Theorem is used as a theoretical tool for proving other theorems (which is why it is perhaps the must important theorem in calculus). Not really for applications. I am sure there are more, but that is the only one I ever saw.
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