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.
Follow Math Help Forum on Facebook and Google+
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?
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.
View Tag Cloud