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Math Help - I don't understand the Intermediate Value Theorem?

  1. #1
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    I don't understand the Intermediate Value Theorem?

    Let f be continuous on the closed interval [-2, 5]. If f(-2) = 3 and f(5) = -7, then the IVt guarentees that:

    a) 7≤f(x)≤3 for all x between -2 and 5
    b) f'(c) = -10/7 for at least one c between [-2, 5]
    c) f(c) = -3 for at least one c between [-2, 5]
    d) f(c) = 0 for at least one c between [-7, 3]
    e) f(x) is continually decreasing between [-2, 5]

    I don't get how to apply the IVT theorem.. My AP exam is in a little over a week. HELP!!!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    all the IVT is saying is that if f(x) is cont on [a,b]

    it takes on all values between f(a) and f(b)
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    So then would the answer be E?
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  4. #4
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    Quote Originally Posted by elpermic View Post
    So then would the answer be E?
    All you know is the f is continuous on the interval. Why couldn't f decrease then increase and then decrease again as we moved from x=-2 \to 5?
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  5. #5
    MHF Contributor Calculus26's Avatar
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    Hint f takes on all values between -7 and 3
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    Quote Originally Posted by danny arrigo View Post
    All you know is the f is continuous on the interval. Why couldn't f decrease then increase and then decrease again as we moved from x=-2 \to 5?

    So then the answer would be A?
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    Quote Originally Posted by elpermic View Post
    So then the answer would be A?
    I'm guessing that (a) has a typo and should read

     <br />
-7 \le f(x) \le 3<br />

    but nothing says that f(x) can be greater than 3 or less than -7. Look at Cal26's second post.
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  8. #8
    MHF Contributor Calculus26's Avatar
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    try c and d also then we will have hit every wrong answer

    sorry for the sarcasm but -10/7 is the only number between -7 and 3
    Last edited by mr fantastic; April 26th 2009 at 07:28 PM. Reason: Merged posts
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    So the answer is B

    How?
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  10. #10
    MHF Contributor Calculus26's Avatar
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    Apologies didn't see the frime on f in b

    and I was reading 3 on c

    Co c is the answer since -3 is between -7 and 3

    that;s what i get for sarcasm
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