The function $$f(x) = \frac{x^{3} + 5x^{2} - 8x}{3}$$ is

positive and monotonically increasing for $$x  \epsilon  (-\infty, \frac{5-\sqrt{57}}{2})$$ and $$x  \epsilon  (\frac{5+\sqrt{57}}{2},+\infty)$$

negative and monotonically decreasing for $$x  \epsilon  (-\infty, \frac{5-\sqrt{57}}{2})$$ and $$x  \epsilon  (\frac{5+\sqrt{57}}{2},+\infty)$$

negative and monotonically increasing for $$x  \epsilon  (-\infty, \frac{5-\sqrt{57}}{2})$$ and positive and monotonically increasing for $$x  \epsilon  (\frac{5+\sqrt{57}}{2},+\infty)$$

positive and monotonically increasing for $$x  \epsilon  (-\infty, \frac{5-\sqrt{57}}{2})$$ ) and negative and monotonically decreasing for $$x  \epsilon (\frac{5+\sqrt{57}}{2},+\infty)$$