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Math Help - help with proof please

  1. #1
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    help with proof please

    How do I prove that that a function f must have a zero on a given interval [a,b]

    thanks,
    D.
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  2. #2
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    Quote Originally Posted by dboyd435 View Post
    How do I prove that that a function f must have a zero on a given interval [a,b]
    One cannot prove a statement that is false.
    As written the statement is false. Please review and correct your post.
    Better yet, post the actual problem using the exact wording.
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  3. #3
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    oh, how was the first statement wrong?


    "prove that f must have a zero on the interval [a,b]. Make sure to give a clear explanation with your proof."

    Thanks.
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  4. #4
    TD!
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    As Plato pointed out, this statement is false.

    Perhaps you're looking at a continuous function which has both signs (so positive and negative) on a given interval [a,b]?
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  5. #5
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    Quote Originally Posted by TD! View Post
    As Plato pointed out, this statement is false.

    Perhaps you're looking at a continuous function which has both signs (so positive and negative) on a given interval [a,b]?
    maybe I should just post the actual function... I think just realized what you have been trying to say.

    the interval [0,3] and the function being f(x)= 2x^3 - 9x^2 + 12x - 7
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  6. #6
    TD!
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    You could explicitly try to find the zero, but that would be "messy" here. My guess is that you've seen the theorem I was referring to in my last post (a continuous function that changes sign in an interval, has a zero in that interval). Can you check that your function is indeed positive and negative on [0,3]?
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  7. #7
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    could I say that because f changes sign between x=2 and x=3 f must have a zero on the interval [0,3] because f must intersect the x-axis in order to chance from (2,-3) to (3,2)
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  8. #8
    TD!
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    Well, I think that's the point. Have you seen that theorem?
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  9. #9
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    probably, I just can not remember it.

    thanks for your help!
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  10. #10
    TD!
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    You're welcome!
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