| Interval | Sign of f\(^{\prime \prime}\) | Conclusion |
|---|---|---|
| \(( -\infty ,-\sqrt{6})\) | negative | \(f\) is concave down on \(( -\infty ,-\sqrt{6})\) |
| \((-\sqrt{6},0)\) | positive | \(f\) is concave up on \(( -\sqrt{6},0)\) |
| \( 0,\sqrt{6}\) | negative | \(f\) is concave down on \(( 0,\sqrt{6})\) |
| \(( \sqrt{6},\infty )\) | positive | \(f\) is concave up on \(( \sqrt{6},\infty )\) |