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Math Help - I can NOT figure out what b is!

  1. #1
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    I can NOT figure out what b is!

    Sorry, i posted the wrong thread title... this is my question:

    Find the equation of a quartic polynomial whose graph is symmetric about the y-axis and has local maxima at (-1, 1) and (1, 1) and a y-intercept of -2.



    I found y=-2x^(4)+5x^(2)-2 but that is not correct... any suggestions?
    Last edited by purplegirl1818; November 4th 2008 at 05:33 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by purplegirl1818 View Post
    Sorry, i posted the wrong thread title... this is my question:

    Find the equation of a quartic polynomial whose graph is symmetric about the y-axis and has local maxima at (-1, 1) and (1, 1) and a y-intercept of -2.



    I found y=-2x^(4)+5x^(2)-2 but that is not correct... any suggestions?
    As it is symmetric it has only even powers of x, and the intercept of -2 means that it is of the form:

    y=ax^4+bx^2-2

    You know that x= \pm 1 give maxima so y'(1)=y'(-1)=0.

    y'=4ax^3+2bx=0

    so the critical points are x=0, x=\pm \sqrt{b/(2a)}=\pm 1, so we must have b=2a, and as the x=\pm 1 critical points must be maxima we have:

    y=-cx^4-2cx^2-2

    for any c>0.

    CB
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