Find the possible values of x, y, z at which?

Find the possible values of x, y, z at which f(x,y,z)=6x^2+7y^2+4z^2-4x-y-3z assumes its minimum value. The point or points at which the function may have a relative minimum is/are:

Don't remember learning this please help!

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  • ?
    Lv 4
    7 years ago
    Favorite Answer

    This problem turns out to be rather easy because the function can be rewritten as

    f(x,y,z)= [6x^2 -4x] + [7y^2 -y] + [4z^2-3z]

    My approach would be to find the value of x that minimizes [6x^2 -4x],

    and then find the value of y that minimizes [7y^2 -y],

    and then find the value of z that minimizes [4z^2-3z]

    That should get you started. Not all functions can be dealt with so easily. Good luck!

  • Anonymous
    4 years ago

    the respond must be x = y = z because of the fact the whole subject is symetrical in all 3 variables, i.e. swopping them around makes no distinction. hence the concern turns into - maximise 3/(2x + a million) subject to the restrictions x > 0 and x = x^2. because of the fact that x = 0 isn't allowed it ought to be x = a million giving a maximum fee of a million.

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