| Interval | Sign of \({f''}\) | Conclusion |
|---|---|---|
| \(( -\infty ,-2-\sqrt{5})\) | positive | \(f\) is concave up on the interval \((-\infty ,-2 - \sqrt{5})\) |
| \((-2-\sqrt{5},-2+\sqrt{5})\) | negative | \(f\) is concave down on the interval \(( -2 -\sqrt{5}, -2+\sqrt{5})\) |
| \((-2+\sqrt{5},\infty)\) | positive | \(f\) is concave up on the interval \(( -2+\sqrt{5},\infty )\) |