| Interval | Sign of \({x^{2}}\) | Sign of \({x-3}\) | Sign of \({f^\prime (x) =4x^{2}(x-3)}\) | Conclusion |
|---|---|---|---|---|
| \((-\infty ,0)\) | Positive \((+)\) | Negative \((-)\) | Negative \((-)\) | \(f\) is decreasing |
| \((0,3)\) | Positive \((+)\) | Negative \((-)\) | Negative \((-)\) | \(f\) is decreasing |
| \((3,\infty)\) | Positive \((+)\) | Positive \((+)\) | Positive \((+)\) | \(f\) is increasing |