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Thread: Max and min values help.

  1. #1
    Dec 2006

    Max and min values help.

    I have this homework question that asks.

    Find the values of a, b, c and d, such that g(x) = ax^3 +bx^2 +cx +d has a local max at (2,4) and a local min at (0,0)

    Its really confusing me in how to approach it.
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  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    Use the equation and its derivative to build a system of equations. It should be rather simplistic.

    The max and min occur at (0,0) and (2,4)

    We have:

    $\displaystyle a(0)^{3}+b(0)^{2}+c(0)+d=0$, therefore, d=0.

    $\displaystyle a(2)^{3}+b(2)^{2}+c(2)+d=4$

    Derivatives must be 0 at extrema:

    $\displaystyle 3a(2)^{2}+2b(2)+c=0$

    $\displaystyle 3a(0)^{2}+2b(0)+c=0$, therefore, c=0.

    Because c and d are 0, that helps whittle things down a good bit.

    We have the following system to solve:

    $\displaystyle 8a+4b=4$
    $\displaystyle 12a+4b=0$

    We find a=-1 and b=3

    Therefore, the polynomial is $\displaystyle g(x)=-x^{3}+3x^{2}$
    Last edited by galactus; Nov 24th 2008 at 05:39 AM.
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