# 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.

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#### Answers 1

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

Tsemo Aristide
May 23, 2020 01:17 AM