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Math Help - Help proving by Mean value theorem

  1. #1
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    Help proving by Mean value theorem

    Hey everybody. The problem goes like this.

    Proof that the line y=11x+16 does not intersect the curve x^3-x in no other points different than (-2,-6) and (4,60) by Mean value theorem.

    Thanks for your help
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  2. #2
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    Start by writing 11x+16 = x^3-x

    What is your attempt at this problem?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Start by writing 11x+16 = x^3-x

    What is your attempt at this problem?
    \[0 =\left (x+2 \right )^{2} \left ( x-4 \right )\]<br />

    I dont know how to proof by Mean value theorem that only two points are the intersection between the line and the curve.

    Thanks for your help.
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by gordo151091 View Post
    \[0 =\left (x+2 \right )^{2} \left ( x-4 \right )\]<br />

    I dont know how to proof by Mean value theorem that only two points are the intersection between the line and the curve.

    Thanks for your help.
    Show that if f(x)=(x+2)^2(x-4) had another solution then f'(x) would have to equal zero somewhere on the appropriate interval.
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