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Math Help - derivations.

  1. #1
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    derivations.

    Prove that the equation x^3-3x+c=0 can't have 2 different soulutions in the segment [0,1].
    It is suggested to find the derivation and to use the way of supposing
    from the contrary.

    Any help is appreciated and sorry for the language.
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  2. #2
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    The derivative of
    <br />
\frac{d}{dx} (x^3 - 3x + C ) = 3x^2 - 3<br />

    which is always negative in the interval [0,1).

    So if the function went through the y=0 line in that interval once, it can't turn around and go back through it to make a second root.
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  3. #3
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    Quote Originally Posted by blertta View Post
    Prove that the equation x^3-3x+c=0 can't have 2 different soulutions in the segment [0,1].
    It is suggested to find the derivation and to use the way of supposing
    from the contrary.

    Any help is appreciated and sorry for the language.
    Intermediate value theorem
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  4. #4
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    Quote Originally Posted by qmech View Post
    The derivative of
    <br />
\frac{d}{dx} (x^3 - 3x + C ) = 3x^2 - 3<br />

    which is always negative in the interval [0,1).

    So if the function went through the y=0 line in that interval once, it can't turn around and go back through it to make a second root.
    i think the function is strictly monotone on [1,0),so there's a unique solution
    b such that b\in [2+c,-2+c].
    no ?
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