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 ?