1. The problem states that the top-right graph represents the first derivative $y' = f'(x)$ of a function $y = f(x)$ defined on $\mathbb{R}$. We need to identify which of the given graphs (a, b, c, d) could represent the original function $f(x)$. 2. Analyze the first derivative graph: It has a vertical asymptote at $x=0$, with $f'(x) \to +\infty$ as $x \to 0^-$ and $f'(x) \to -\infty$ as $x \to 0^+$. This means the slope of $f(x)$ becomes very large positive just before $x=0$ and very large negative just after $x=0$. 3. Interpretation: The function $f(x)$ must have a sharp peak or cusp at $x=0$ because the derivative changes from very large positive to very large negative abruptly. 4. Check each candidate graph: - Graph (a): Increasing curve from below x-axis upwards, no sharp peak at $x=0$. - Graph (b): Passes through origin and increases smoothly, no sharp peak. - Graph (c): 'V' shape opening upwards, has a sharp minimum at $x=0$. - Graph (d): Inverted 'V' shape opening downwards, has a sharp maximum at $x=0$. 5. Since $f'(x)$ goes from $+\infty$ to $-\infty$ at $x=0$, $f(x)$ has a sharp maximum at $x=0$, matching graph (d). 6. Therefore, the graph that may represent $f(x)$ is graph (d). Final answer: Graph (d) represents the function $f(x)$ whose first derivative is given by the top-right graph.