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.
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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.
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