Let $f:[0, \infty) \longrightarrow \mathbb R$ be a continuous function which converges for $t \rightarrow +\infty$.
What can you say about existence of extrema and boundedness of the function f?
Exsitence of extrema and boundedness of a function
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real-analysis
functions
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0What can you say about these matters? How about some thoughts, some ideas, some context, some work? – 2017-01-18
1 Answers
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If $\Vert f \Vert = \sup_{x \in [0,\infty)} \frac{|f(x)|}{|x|} < \infty$ Holds it is bounded. If the image of $f$ is a compact set it attains its maximum and minimum
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0What does $|f(x)|/|x|$ have to do with it? – 2017-01-18