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Thread: Need help deciphering a function

  1. #1
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    Need help deciphering a function

    Let P(x) = x^4+ax^3+bx^2+cx+d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative maximum at (0,1), and has an absolute minimum at (q, -3).

    a) Determine the values of a,b,c, and d

    b) Find all possible values of q

    Thanks if anybody can help.
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  2. #2
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    Quote Originally Posted by alakaboom1 View Post
    Let P(x) = x^4+ax^3+bx^2+cx+d. The graph of y = P(x) is symmetric with respect to the y-axis, has a relative maximum at (0,1), and has an absolute minimum at (q, -3).

    a) Determine the values of a,b,c, and d

    b) Find all possible values of q

    Thanks if anybody can help.
    Symmetrix with respect to the y-axis means that $\displaystyle P(x)=P(-x)$ , which forces $\displaystyle a$ and $\displaystyle c$ to be zero.

    So now you have:

    $\displaystyle P(x)=x^4+bx^2+d$


    So $\displaystyle P'(x)=4x^3+2bx$, and so the extrema are at $\displaystyle x=0$, and $\displaystyle x=\pm \sqrt{-b/2}$ , so from the latter we have $\displaystyle -b/2=9$, or $\displaystyle b=-18$.

    Can you finish from there?

    CB
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