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Math Help - Help finding the extreme values

  1. #1
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    Help finding the extreme values

    Hello,

    I need to use the lagrange method to find the extreme values of
    f(y,z)=z^3+yz

    with this condition

    y+3z+24=0

    I got this system of equations
    z-\lambda=0 (1)
    3z^2+y-3\lambda=0 (2)
    y+3z+24=0 (3)

    And I tried to define y in terms of z, y=3z-3z^2 and insert in (3)
    But I get the wrong answer after solving the new equation.

    The right answer is
    (4,-36) and (-2,-18)

    Would anyone mind to explain how to get to the right answer?

    Thanks
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Leeds, UK
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    Quote Originally Posted by sebasto View Post
    I got this system of equations
    z-\lambda=0 (1)
    3z^2+y-3\lambda=0 (2)
    y+3z+24=0 (3)

    And I tried to define y in terms of z, y=3z-3z^2 and insert in (3)
    But I get the wrong answer after solving the new equation.

    The right answer is
    (4,-36) and (-2,-18)
    If you substitute y=3z-3z^2 in (3), you should get 3z-3z^2+3z+24=0, so that 3z^2 - 6z -24 = 0, with solutions z = 4, 2. The given answer appears to list the coordinates in anti-alphabetical order, (z,y) rather than (y,z)!
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