1. The problem asks to identify which graph represents the derivative $f'(x)$ of the given function $y=f(x)$ shown in the top-right graph. 2. The original function $f(x)$ starts near $(x=-1.5, y=1)$, rises to a peak near $(x=0, y=3)$, then falls below the x-axis near $(x=1.5, y=-2)$. 3. Key points to analyze for $f'(x)$: - At the peak of $f(x)$ (near $x=0$), the slope is zero, so $f'(0)=0$. - For $x < 0$, $f(x)$ is increasing, so $f'(x) > 0$. - For $x > 0$, $f(x)$ is decreasing, so $f'(x) < 0$. 4. Checking the candidate graphs: - Graph a: Descending line from about $(x=-1, y=4)$ to $(x=2, y=0)$, so $f'(x)$ decreases from positive to zero. - Graph b: Ascending line from about $(x=0, y=-2)$ to $(x=2, y=2)$, so $f'(x)$ goes from negative to positive, which contradicts the original function's behavior. - Graph c: A curve starting below x-axis, rising to a peak near $x=-1$, then descending through x-axis near $x=1.5$. This shape suggests $f'(x)$ is positive before $x=0$ and negative after, crossing zero near $x=0$. - Graph d: Descending line from about $(x=-1, y=2)$ to $(x=2, y=-2)$, similar to graph a but with different intercepts. 5. Since $f'(x)$ must be positive before $x=0$, zero at $x=0$, and negative after $x=0$, graph c best matches this behavior. 6. Therefore, the curve representing $f'(x)$ is graph c. Final answer: Graph c represents the curve of $f'(x)$.