Interval | Sign of 4x | Sign of (x2−1)1/3 | Sign of f′(x)=4x3(x2−1)1/3 | Conclusion |
---|---|---|---|---|
(−∞,−1) | Negative (−) | Positive (+) | Negative (−) | f is decreasing on (−∞,−1) |
(−1,0) | Negative (−) | Negative (−) | Positive (+) | f is increasing on (−1,0) |
(0,1) | Positive (+) | Negative (−) | Negative (−) | f is decreasing on (0,1) |
(1,∞) | Positive (+) | Positive (+) | Positive (+) | f is increasing on (1,∞) |