| Interval | Sign of f\(^{\prime \prime}\) | Conclusion |
|---|---|---|
| \((-\infty ,0)\) | positive | \(f\) is concave up on \((-\infty ,0)\) |
| \(\left( 0,\dfrac{4}{3}\right)\) | negative | \(f\) is concave down on \(\left( 0,\dfrac{4}{3}\right)\) |
| \(\left( \dfrac{4}{3},\infty \right)\) | positive | \(f\) is concave up on \(\left( \dfrac{4}{3},\infty \right)\) |