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)`.