1. The problem asks us to determine which graph could represent the second derivative $f''(x)$ of a function $f(x)$ given its curve. 2. The given $f(x)$ curve crosses the x-axis at points $-a$ and $a$, indicating roots of $f(x)$. 3. To find $f''(x)$, recall that $f''(x)$ is the derivative of $f'(x)$, which is the slope of $f(x)$. 4. Analyze the shape of $f(x)$: it is positive between $-a$ and $a$ and crosses zero at these points. 5. The first derivative $f'(x)$ will be zero at local maxima and minima of $f(x)$, and $f''(x)$ indicates concavity: positive where $f(x)$ is concave up, negative where concave down. 6. Since $f(x)$ crosses the x-axis at $-a$ and $a$, and assuming it is a cubic-like shape, $f''(x)$ will have zeros at these points and change sign. 7. The second derivative $f''(x)$ graph should have arrows indicating the concavity changes: positive concavity corresponds to $f''(x)>0$ and negative concavity to $f''(x)<0$. 8. Among the options (a), (b), (c), and (d), option (c) shows the correct orientation of arrows consistent with the concavity changes of $f(x)$. 9. Therefore, the graph in option (c) represents the function $f''(x)$. Final answer: The graph labeled (c) represents $f''(x)$.