| Interval | Sign of \({x-2}\) | Sign of \({x^{1/3}}\) | Sign of \({f^\prime (x) =\dfrac{5}{3}\left( {\dfrac{x-2}{x^{1/3}}}\right) }\) | Conclusion |
|---|---|---|---|---|
| \((-\infty ,0)\) | Negative \((-)\) | Negative \((-)\) | Positive \((+)\) | \(f\) is increasing |
| \((0,2)\) | Negative \((-)\) | Positive \((+)\) | Negative \((-)\) | \(f\) is decreasing |
| \((2,\infty)\) | Positive \((+)\) | Positive \((+)\) | Positive \((+)\) | \(f\) is increasing |