Question Number 212204 by liuxinnan last updated on 06/Oct/24
$${f}\left({x}\right)\:{is}\:{continous}\:{and} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=−\infty \\ $$$${prove}\:{max}\left({f}\left({x}\right)\right)\:{exist} \\ $$
Commented by mr W last updated on 06/Oct/24
$${that}'{s}\:{not}\:{true}.\:{a}\:{counter}−{example}: \\ $$$${f}\left({x}\right)=−{x}^{\mathrm{3}} \\ $$
Commented by loredcs2357 last updated on 06/Oct/24
$$\mathrm{I}\:\mathrm{think}\:\mathrm{he}\:\mathrm{means}\:\underset{{x}\rightarrow\pm\infty} {\mathrm{lim}}{f}\left({x}\right)=−\infty.\:\mathrm{In}\:\mathrm{this}\:\mathrm{case}\:\mathrm{it}'\mathrm{s}\:\mathrm{true}. \\ $$