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Math Help - Can Someone Explain the Mean Value Theorem to me?

  1. #1
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    Can Someone Explain the Mean Value Theorem to me?

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  2. #2
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    Quote Originally Posted by drain View Post
    Let f be continous on [a,b] and differenciable on (a,b).

    There shall exists a point x in (a,b) such that,

    f'(x) = MEAN VALUE.

    The mean value is the average, that is,

    (f(b)-f(a))/(b-a)

    Hence,

    f'(x) = (f(b)-f(a))/(b-a)
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    lol I get that. I mean why is it useful? Like some sorts of applications of it?
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    Quote Originally Posted by drain View Post
    I mean why is it useful? Like some sorts of applications of it?
    What do you mean?

    It is not useful in applications. It is useful in proofs. It is perhaps, the most important theorem in calculus. So many proofs are derived from it.
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  5. #5
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    Quote Originally Posted by ThePerfectHacker View Post
    What do you mean?
    Is this a math joke?

    I guess my question is like, what sorts of problems will we be asked to solve with it? (In a first semester calculus course)
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    Quote Originally Posted by drain View Post
    Is this a math joke?
    Yes. I have a talent for coming up with math jokes (though not necessarily funny).

    For example, look at my signature. "Elementary Complex Analysis". There is a topic in math called Complex analysis, thus if you call your book like that it sounds like it is both elementary and complicated. I found that funny.
    I guess my question is like, what sorts of problems will we be asked to solve with it? (In a first semester calculus course)
    You be asked to find what c makes the mean value.

    Example,

    Given f(x)=x^2 on [-1,1]
    Find a number c in (-1,1) such that,
    f'(c)=Mean Value
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  7. #7
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    Thanks man. BTW, are you from the past? I didn't know the USSR was still around~!
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  8. #8
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    Lightbulb

    Quote Originally Posted by drain View Post
    Thanks man. BTW, are you from the past? I didn't know the USSR was still around~!
    I came from the Union of Soviet Socialist Republic. But its own power destroyed it (like a blackhole) so today it no longer exists. But I can still say I came from there.
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  9. #9
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    Well they have good boxers from that area.
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