I don't have much to ask. Just wanted to know if it is actually possible to write out the minimum value of the function $f(x)=x^3$ whenever it is defined over $(1,10)$ (open interval).
You can choose any other function (this came to my mind first!). So I know that the range of it is $(1,1000)$ for the specified domain. So does 1 count as the minimum value or do we say that "minimum and maximum do not exist" ?