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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 ?

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# Homework Help: Global minimum

Can you offer guidance or do you also need help?

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