Suppose that f:R→R is continuous on R and that limx→−∞f(x)=limx→+∞f(x)=k
Prove that f is bounded and if there exist a point x0∈R such that f(x0)>k, then f attains a maximum value on R.
Edit by non OP. The OP seems to be a new user that posted the same question twice in less than 2 hours, both on MSE.
Real analysis continuous functions
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