Let $f$ be a continuous funtion on interval $I=[a,b]$. Then $f$ has the absolute maximum value and $f$ attains it at least once in $I$. Also, $f$ has the absolute minimum value and attains it at least once in $I$.
This is a theorem.
A constant function is also continuous, but I can't find any absolute maximum or minimum value in it. Can someone help me with this condition?
Best Answer
Let $f(x)=c$ for all $x\in [a,b]$ then $f(x) \leq c$ for all $x\in [a,b]$ and $f(x) \geq c$ for all $x\in [a,b]$, so in fact, any $x\in [a,b]$ is an absolute maximum and absolute minimum.