It's the open interval. The function increases over any interval on which its derivative is positive. We have
[tex]f(x)=x^2\implies f'(x)=2x[/tex]
and [tex]f'(x)>0[/tex] for [tex]x>0[/tex]. So [tex]f(x)[/tex] is increasing on [tex]x>0[/tex], or [tex](0,\infty)[/tex].
