Answer by MJD for Coming up with a counter example - calculus
There are two ways that a function can fail to achieve a maximum:It can increase to $\infty$It can approach the maximum, without quite reaching it, as $1-\frac1x$ increases toward $1$ without getting...
View ArticleAnswer by José Carlos Santos for Coming up with a counter example - calculus
You can take, for instance, $f(x)=\sin(x)\arctan(x)$. Its supremum and its infimum are $\pm\pi/2$, but none of them is reached. Besides, it is continuous and bounded (for each $x\in[0,\infty)$,...
View ArticleComing up with a counter example - calculus
I have to come up with a counter example for the following statement:Let $f$ be a function $f: [0,\infty)\longrightarrow R$, continuous and bounded. Prove that it receives either a minimum or a maximum...
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