Is this true: If $f:(a,b)\to\Bbb{R}$ is strictly increasing, then $f$ does not attain its maximum nor minimum in $(a,b)$?

by Wybie   Last Updated May 23, 2020 01:20 AM

Is this true: If $f:(a,b)\to\Bbb{R}$ is strictly increasing, then $f$ does not attain its maximum nor minimum in $(a,b)$?

I need to verify if this statement is true or false.

Making the graph it looks true to every graph I draw, but I am not sure how to prove this or find a counterexample...

Thanks.

Tags : real-analysis


Answers 1


Suppose $f$ attains its maximum, in $u$, $u<b$, there exists $u<v<b$, $f(u)<f(v)$ contradiction

Tsemo Aristide
Tsemo Aristide
May 23, 2020 01:17 AM

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