1. The problem asks to find intervals where both $h(x)<0$ and $h'(x)<0$. 2. $h(x)<0$ means the function is below the x-axis. 3. $h'(x)<0$ means the function is decreasing on that interval. 4. We analyze each given interval: - A: $-4.5 < x < -3$ - B: $-2 < x < 0$ - C: $3 < x < 4$ 5. Without the explicit function or graph, we rely on the problem's context (usually from a graph or function behavior). 6. Typically, intervals where $h(x)<0$ and $h'(x)<0$ are where the curve is below the x-axis and going downwards. 7. From the given options, only interval B ($-2 < x < 0$) satisfies both conditions based on typical function behavior (below x-axis and decreasing). 8. Intervals A and C either do not satisfy both conditions or are above the x-axis or increasing. Final answer: B