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Math Help - Find ans classify the stationary points for the following functions

  1. #1
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    Find ans classify the stationary points for the following functions

    Find ans classify the stationary points for the following functions:

    Q= 5㏑L + 2㏑K - 0.1L - 0.4K
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  2. #2
    MHF Contributor
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    If that is
    Q = 5L^2 +2K^2 -0.1L -0.4K
    then,
    get the partial derivatives of Q with respect to L and K, and set those to zero.

    Let me express "partial deivative of Q with respect to L" as DQ/DL, so,
    DQ/DL = 10L -0.1
    0 = 10L -0.1
    L = 0.1/10 = 0.01

    DQ/DK = 4K -0.4
    0 = 4K -0.4
    K = 0.4/4 = 0.1

    Thus, for those values,
    Q = 5(0.01)^2 +2(0.1)^2 -0.1(0.01) -0.4(0.1) = -0.0205

    Hence, if the point is expressed in (L,K,Q), then,
    (0.01, 0.1, -0.0205)
    is the stationary point.

    To check if if it is maximum, minimum or a saddle point, we look at the second partial derivatives.

    D/DL of DQ/DL = 10 ......positive
    D/DK of DQ/DK = 4 .......positive also
    Meaning, the stationary point could be a minimum.

    Let's chect the mixed partial,
    D/DL of DQ/DK = 0

    So
    (10)(4) -0 = 40 ......positive
    Meaning, the stationary point is really a minimum point.
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