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Math Help - maximum and minimum

  1. #1
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    Question maximum and minimum

    Basically i'v been given the following function

    Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.


    and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

    So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
    From that i found that:
    x= 77/8
    y=8/11
    z=2/7


    The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

    any help? Thankz
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  2. #2
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    Quote Originally Posted by dopi View Post
    Basically i'v been given the following function

    Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.


    and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

    So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
    From that i found that:
    x= 77/8
    y=8/11
    z=2/7


    The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

    any help? Thankz
    Okay, this type of question is not covered in a standard Calculus sequence in college. Because we require a test to determine whether it is a maximum or a minimum or neither.
    However, I believe the more general test (I never used it thus I do not know) is a 3x3 Determinant of a Hessian Matrix.
    Keylogger.Netbus.Ewido
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by dopi View Post
    Basically i'v been given the following function

    Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.

    and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

    So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
    From that i found that:
    x= 77/8
    y=8/11
    z=2/7

    The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

    any help? Thankz
    What Perfect hacker said, but also:

    Choose a unit vector u=(cos(theta)cos(phi), cos(theta)sin(phi), sin(theta))
    then let (a,b,c)=(x,y,z)+lambda*u. Then if f(x,y,z) is a maximum (minimum)
    then f((x,y,z)+lambda*u) considered as a function of lambda will be a maximum
    (minimum) for all theta and phi.

    RonL
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  4. #4
    Super Member Rebesques's Avatar
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    ...Did you manage to find da minima and maxima and da saddle points? CheerZ!
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  5. #5
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    Smile thankz

    Quote Originally Posted by Rebesques View Post
    ...Did you manage to find da minima and maxima and da saddle points? CheerZ!
    hey yeah i decided to use the hessian matrix method ...i found an example on the net and used that ...thankz
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