# Math Help - Supremum Of A function

1. ## Supremum Of A function

If F:R-->R be defined by f(x)= x^2/(x^2 + 1) for all x (- R. Then the function attains supremum. True or False. Give reason.

2. ## Re: Supremum Of A function

Have you looked at the graph of this function? That should give you a hint.
Also look at the derivative of the function. What does that tell you?

3. ## Re: Supremum Of A function

Well I think that the statement is false. It attains infimum at x=0. x=0 is the only critical point. However it tends to 1 as x tends to infinity.. so i think it does not achieve a supremum.