1. The problem states: "The third derivative is under 16." We need to understand what this means and how to work with it. 2. The third derivative of a function $f(x)$ is denoted as $f^{(3)}(x)$ or $\frac{d^3}{dx^3}f(x)$. It represents the rate of change of the second derivative. 3. Saying "the third derivative is under 16" means: $$f^{(3)}(x) < 16$$ for all relevant $x$. 4. Without a specific function, we cannot compute the third derivative explicitly. However, if you have a function $f(x)$, you can find its third derivative by differentiating three times: $$f^{(3)}(x) = \frac{d}{dx}\left(\frac{d}{dx}\left(\frac{d}{dx}f(x)\right)\right)$$ 5. To check if $f^{(3)}(x) < 16$, compute $f^{(3)}(x)$ and verify the inequality. 6. If you provide a specific function, I can help compute the third derivative and check the condition. Final answer: The third derivative $f^{(3)}(x)$ must satisfy $$f^{(3)}(x) < 16$$.