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Math Help - Problem on finding values

  1. #1
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    Problem on finding values

    I'm having trouble with doing this problem, and I'm not really sure how to even first go about it. All I was able to figure out is that d=1. If someone could explain this problem to me step by step that would be really appreciated, thank you!

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

    A) Determine the values a, b, c, d and using these values write an expression for P(x)

    B) Find all possible values of q
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  2. #2
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  3. #3
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    Quote Originally Posted by choi_siwon View Post
    I'm having trouble with doing this problem, and I'm not really sure how to even first go about it. All I was able to figure out is that d=1. If someone could explain this problem to me step by step that would be really appreciated, thank you!

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

    A) Determine the values a, b, c, d and using these values write an expression for P(x)

    B) Find all possible values of q
    Since it has a relative max at (0,1)

    P'(0)=0

    P'(x)=4x^3+3ax^2+2bx+c \implies P'(0)=0=c

    If P is symmetric with the y axis then

    P(x)=P(-x) for ALL values of x.

    x^4+ax^3+bx^2+1=x^4-ax^3+bx^2+1

    2ax^3=0 this can only be zero for all values of x if a=0

    P(x)=x^4+bx^2+1 \implies P'(x)=4x^3+2xb

    q=P(-3)=81+9b+1

    P'(-3)=0=-108-6b \implies b=-\frac{54}{3}=-18

    q=81-162+1=-80
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  4. #4
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    Thanks for the link skeeter!

    And thank you so much TheEmptySet! I understand it now.
    Last edited by choi_siwon; November 30th 2008 at 03:47 PM.
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