What is the interval over which the function $f(x)=6x-x^2,x>0$ is increasing?

A function $f(x)$ is increasing on an interval if its derivative $f^{\prime }(x)>0$.Given: $f(x)=6x-x^2$ Differentiating with respect to $x$:
$$f^{\prime }(x)=6-2x$$
For the function to be increasing:
$$f^{\prime }(x)>0⟹6-2x>0$$
$$2x<6⟹x<3$$
Since it is given that $x>0$, the interval is:
$$0<x<3$$
In interval notation, this is $(0,3)$.