Critical Points and Intervals of Increase

I. For $$f(x)= x^3 - 3*x^2 + 4$$, the derivative is $$f'(x)= 3*x^2 - 6*x$$ which yields critical points at $$x=0$$ and $$x=2$$.

II. The function f(x) is increasing on the intervals $$(-\infty, 0)$$ and $$(2, \infty)$$.

III. f(x) is decreasing on the interval $$(0,2)$$.

Which of the above statements is/are correct?