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**Does this Fxy have a global Min?**

Heres the question:

Consider the function fxy= x+y+9/x+1/y. Determine all the local max min and saddle points. DOes f have any global maximum points in the region R where x,y>0 Explain algebraically.

So I found only one critical point, 3,1 and found it to be a local min.

As for the global part, I said NO, because the function does not have a boundry x and y goto infinity and this function does not the sort of parabolic shape to have a natural global max or min.

Is that right? How could I be more graceful with my answer?

Thanks geniuses