query: Trouble in proving that a continuous function vanishing at $\pm\infty$ attains at least its maximum or minimum.
positive_passages.docid: 154247
positive_passages.text: Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
negative_passages.docid: 57014
negative_passages.text: Existence of a power series converging non-uniformly to a continuous function
negative_passages.docid: 128975
negative_passages.text: Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 105768
negative_passages.text: Proof involving absolute value and maximums
negative_passages.docid: 141529
negative_passages.text: Proving existence of a minimum
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 96273
negative_passages.text: Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
negative_passages.docid: 148931
negative_passages.text: Constructing a function that is continuous and has a max on an open interval, but is not necessarily increasing immediately to the left of the max.
negative_passages.docid: 23436
negative_passages.text: $f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
negative_passages.docid: 33308
negative_passages.text: Unique local extremum is absolute extremum for continuous functions
negative_passages.docid: 69066
negative_passages.text: $\epsilon{\rm -}\delta$ proof of the discontinuity of Dirichlet's function
negative_passages.docid: 12523
negative_passages.text: Supremum of a Continuous Function is Continuous
negative_passages.docid: 36099
negative_passages.text: Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$
negative_passages.docid: 154881
negative_passages.text: Question on differentiability of a continuous function
negative_passages.docid: 88586
negative_passages.text: show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant
negative_passages.docid: 40576
negative_passages.text: Intermediate value property problem and continuous function