| Interval | Sign of f\(^\prime(x)\) | Conclusion |
|---|---|---|
| \((-\infty ,0)\) | positive | \(f\) is increasing on \((-\infty ,0)\) |
| \((0,3)\) | negative | \(f\) is decreasing on \((0,3)\) |
| \(\left( 3,6\right)\) | negative | \(f\) is decreasing on \(\left( 3,6\right)\) |
| \(\left( 6,\infty \right)\) | positive | \(f\) is increasing on \(\left(6,\infty \right) \) |