| Interval | Sign of \({x-1}\) | Sign of \({x-2}\) | Sign of \(f^\prime (x) = 6( x-2) ( x-1)\) | Conclusion |
|---|---|---|---|---|
| \(( -\infty ,1)\) | Negative \((-)\) | Negative \((-)\) | Positive \((+)\) | \(f\) is increasing |
| \((1,2)\) | Positive \((+)\) | Negative \((-)\) | Negative \((-)\) | \(f\) is decreasing |
| \((2,\infty )\) | Positive \((+)\) | Positive \((+)\) | Positive \((+)\) | \(f\) is increasing |