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Math Help - Intermediate Value Theorem

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    Intermediate Value Theorem

    Maybe its just me, but I feel like this question is worded wrong in some way.

    Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

    the cubed root of x=1-x, from 0 to 1.

    I really don't even know where to start. My notes tell me what to do relatively well, but they also tell me that i need a constant in which to solve for. Help please?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ExCaLiBuR View Post
    Maybe its just me, but I feel like this question is worded wrong in some way.

    Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.

    the cubed root of x=1-x, from 0 to 1.

    I really don't even know where to start. My notes tell me what to do relatively well, but they also tell me that i need a constant in which to solve for. Help please?
    I would assume this is asking show that f(x)=x+\sqrt[3]{x}-1=0 for some x\in[0,1]. It doesn't strike you as odd that f(0)<0,f(1)>0?
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    Quote Originally Posted by Drexel28 View Post
    I would assume this is asking show that f(x)=x+\sqrt[3]{x}-1=0 for some x\in[0,1]. It doesn't strike you as odd that f(0)<0,f(1)>0?
    I understand that, but where does that fit into showing that there is a root of the equation? I'm sorry if I'm being extremely difficult, but I'm new to this
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ExCaLiBuR View Post
    I understand that, but where does that fit into showing that there is a root of the equation? I'm sorry if I'm being extremely difficult, but I'm new to this
    I mean this in the most non-condescending way possible. Write out the hypothesis and conclusion the the IVT. I bet half way through it will hit you.
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    Quote Originally Posted by ExCaLiBuR View Post
    I understand that, but where does that fit into showing that there is a root of the equation? I'm sorry if I'm being extremely difficult, but I'm new to this
    In fact it is very clear. If f(c)=0 then c is a root of the equation f(x)=0.
    What do you not understand about that?
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    Quote Originally Posted by Drexel28 View Post
    I mean this in the most non-condescending way possible. Write out the hypothesis and conclusion the the IVT. I bet half way through it will hit you.
    i really have no idea what you are talking about haha. I've tried to graph it out and my professor said that there is a number c in (0,1) such that f(c) = k (on the graph). The question confuses me as to where the c and k come into play.
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    Quote Originally Posted by Plato View Post
    In fact it is very clear. If f(c)=0 then c is a root of the equation f(x)=0.
    What do you not understand about that?
    That does make sense, I just don't understand where you got f(c)=0 from? I mean- where do you get the root of the equation, are there more than one answers?
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    Quote Originally Posted by ExCaLiBuR View Post
    That does make sense, I just don't understand where you got f(c)=0 from? I mean- where do you get the root of the equation, are there more than one answers?
    The key to this is that the graph of a continuous function cannot have a ‘hole’ in it.
    If f is continuous on [a,b] and C is between f(a)~\&~f(b) then the graph cannot ‘skip’ over C.
    So there is a c,~a\le c\le b such that f(c)=C. No skipping.
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