1

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?

alitran
  • 19
  • there's a problem with what you mean by, for instance, division in $\mathbb{R}^n$. Can you divide $(1,1)$ by $(1,2)$? So how is $f$ defined for $x\in \mathbb{R}^n$? And how do you order elements in $\mathbb{R}^n$ so you can talk about "infimum"? – user340297 Jun 19 '16 at 11:14
  • That's my problem. I only know how to define Supremum and Infimum for x in R. I have no idea what it changes if x is in R^n. I also couldn't find any materials that would help me. – alitran Jun 19 '16 at 11:21
  • where did you find this exercise from? I don't think there's any meaningful way of defining orders on $\mathbb{R}^n$ so as to define infimum or supremum, nor I know some ways of defining division in multidimensional space. I don't think this problem is well-posed – user340297 Jun 19 '16 at 11:23
  • it is not in any textbook. we just got it dictated to solve. Could it be a mistake? – alitran Jun 19 '16 at 11:35

0 Answers0