| Interval | Sign of f\(^{\prime \prime}\) | Conclusion |
|---|---|---|
| \((0,0.63)\) | positive | \(f\) is concave up on the interval \(( 0,0.63)\) |
| \(( 0.63,2.51)\) | negative | \(f\) is concave down on the interval \(( 0.63,2.51)\) |
| \(( 2.51,4.14)\) | positive | \(f\) is concave up on the interval \(( 2.51,4.14)\) |
| \(( 4.14,5.28)\) | negative | \(f\) is concave down on the interval \(( 4.14,5.28)\) |
| \(( 5.28,2\pi )\) | positive | \(f\) is concave up on the interval \(( 5.28,2\pi )\) |