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Global minimum

  1. Apr 2, 2005 #1
    hi. ive got another problem.

    i have the function :
    f(x,y) = x^2 + y^2 +(xy)^-1

    iam supposed to use the "extremalvalue theorem" to show that this function have a global minimum on the area x>= 0.1 ,y>= 0.1

    and i also need to argue if the same thing is satisfied for x>0 and y>0.

    for this one , there is given a hint : to set u=1/x and v=1/y..and then iam supposed to look at the function f(x,y) = g(u,v)

    First of all , I tried to find the partials which i think is :
    f_x = 2x - (1/(x^2*y))
    f_y = 2y -(x/(y^2*x))

    how can i do this? Can anyone help me?

    i got that the function has local minimum in the point x=y= 1/(2^(1/4))
    if this is a local minimum , can i then directly say that it has to be a global minimum for x>0 and y>0 ?
  2. jcsd
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