Supremum/Infimum if x in R^n

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there is a function f(x)=(3+x^2)/(5+x^4). I should find the Supremum and Infimum BUT for x of R^n.

I dont understand what x in R^n changes in this situation? I can see that the Supremum in this case would be f(x)=2/3 and the Infimum f(x)=0. I check it by looking for the points where f'(x)=0 and then I put those x points in my f(x) to get the y. This is in case of x in R. What about x in R^n?