Question

For what interval is the function f(x) = x^2 increasing? Is it [0,infinity) or (0, infinity)?

Answer 1

It's the open interval. The function increases over any interval on which its derivative is positive. We have

$f(x)=x^2\implies f'(x)=2x$

and $f'(x)>0$ for $x>0$. So $f(x)$ is increasing on $x>0$, or $(0,\infty)$.