1. **Stating the problem:** We need to find the solution set for the inequality $f'(x) < 0$. This involves identifying where the derivative of the function $f(x)$ is negative. 2. **Understanding the derivative:** The derivative $f'(x)$ represents the slope of the tangent line to the graph of $f(x)$. When $f'(x) < 0$, the function is decreasing. 3. **Analyzing the graph:** From the description, the graph has two branches, one descending steeply and another curving upwards after dipping below the x-axis. 4. **Solution approach:** Identify intervals where the graph of $f(x)$ is going down (slopes are negative). These intervals correspond to $f'(x)<0$. 5. Without the exact function or precise graph data, general regions where the function decreases need to be pointed out from the graph visualization. **Final answer:** If the function $f(x)$ decreases on intervals $I_1, I_2, \dots$, then $$f'(x) < 0 \text{ for } x \in I_1 \cup I_2 \cup \dots$$ You need to inspect the graph to mark these intervals explicitly.