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Math Help - 14th Degree Polynomial Help!

  1. #16
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    Re: 14th Degree Polynomial Help!

    I worked through hundreds and hundreds of simple functions. But I can't work it out. Please Help!
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  2. #17
    MHF Contributor MarkFL's Avatar
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    Re: 14th Degree Polynomial Help!

    Then you should know to evaluate your original function at the roots of its derivative having odd multiplicity.
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  3. #18
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    Re: 14th Degree Polynomial Help!

    I already worked through many and many simpler functions. I can't seem to get this one. Please HELP!
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  4. #19
    MHF Contributor MarkFL's Avatar
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    Re: 14th Degree Polynomial Help!

    What is preventing you from evaluating the function at the roots of the derivative?
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  5. #20
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    Re: 14th Degree Polynomial Help!

    Quote Originally Posted by Jeka View Post
    Sorry, I don't get it. Sorry.

    Can you PLEASE do an example, on my function.
    PLEASEEEEEEEEEEEEEEEEEEEEE!
    I beg you!
    Please!!!!!!!!
    I agree with MarkFL2. For example, let f(x) = x^3 - 2x^2 - 11x + 12. Where are the turning points?
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  6. #21
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    Re: 14th Degree Polynomial Help!

    I was told from another person, that there are turning points at around

    x = 4.344, x = 0.290, x = -2.492

    Its close, but exact. Its somewhere around there.
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  7. #22
    MHF Contributor MarkFL's Avatar
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    Re: 14th Degree Polynomial Help!

    Those are 3 of the critical values, the same which I gave many posts ago, only to a greater degree of accuracy.
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  8. #23
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    Re: 14th Degree Polynomial Help!

    MarkFL2
    Then, can you please help me solve this algebraically? please?

    7x^(3)-15x^(2)-72x+22

    Please help me find all the x-values, the full explanation and working out. Please!
    Please!
    Thanks
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  9. #24
    MHF Contributor MarkFL's Avatar
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    Re: 14th Degree Polynomial Help!

    I have computed approximations for the 3 roots of the cubic polynomial using Newton's method to 12 digits, given you a link to an article about how the method works, given you a link to an article about how to obtain the exact value of the roots. I'm happy with the approximations...I'm not going to use the cubic formula...it is messy and time consuming, and not worth the effort, in my opinion. Substituting the huge cumbersome values into the original function would not be fun either.

    So, take the roots of the derivative of odd multiplicity, which have all been found, and evaluate the original function at these roots. These are your turning points.
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  10. #25
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    Re: 14th Degree Polynomial Help!

    MarkFL2
    How about you give me your email, and lets talk there?
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  11. #26
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    Re: 14th Degree Polynomial Help!

    Can anyone please help me solving this with full explanation and working out?

    7x^(3)-15x^(2)-72x+22

    If not, can anyone tell me how or what would help solve the problem.
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  12. #27
    Senior Member MaxJasper's Avatar
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    Re: 14th Degree Polynomial Help!

    That is called a polynomial!
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  13. #28
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    Re: 14th Degree Polynomial Help!

    OK, whatever. But can you solve it?
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  14. #29
    MHF Contributor MarkFL's Avatar
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    Re: 14th Degree Polynomial Help!

    Are you not satisfied with the approximations I gave using Newton's method?
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