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Math Help - show solution exists in the interval

  1. #1
    Member sluggerbroth's Avatar
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    show solution exists in the interval

    2x^(7)=1-x (0,1)????
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    MHF Contributor Reckoner's Avatar
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    Re: show solution exists in the interval

    Quote Originally Posted by sluggerbroth View Post
    2x^(7)=1-x (0,1)????
    Are you familiar with the Intermediate Value Theorem?

    We have 2x^7+x-1=0. Consider the function f(x)=2x^7+x-1. We know that f(0) = -1 and f(1) = 2. Since f is continuous, what does this tell us?
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  3. #3
    Member sluggerbroth's Avatar
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    Re: show solution exists in the interval

    i'm just learning IVT. not sure what ypu are saying about interval (0,1)
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  4. #4
    Junior Member Sarasij's Avatar
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    Re: show solution exists in the interval

    Quote Originally Posted by sluggerbroth View Post
    i'm just learning IVT. not sure what ypu are saying about interval (0,1)
    What Reckoner pointed is that there is some "c" where 0 < c < 1 for which f(c) must be 0. In other words there exists atleast one root in (0,1).
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