1. The problem asks us to analyze the curve of the function $f''(x)$ and determine which statements about the function $f$ are true. 2. Recall that $f''(x)$ is the second derivative of $f(x)$, which tells us about the concavity of $f$: - If $f''(x) > 0$, then $f$ is convex upward (concave up) on that interval. - If $f''(x) < 0$, then $f$ is concave downward (convex downward) on that interval. - If $f''(x)$ changes sign at $x = a$, then $f$ has an inflection point at $x = a$. 3. From the description, the graph of $f''(x)$ is a horizontal line at $y=4$ for all $x$ (since the arrow at $y=4$ labeled $f''(x)$ extends horizontally). 4. Since $f''(x) = 4 > 0$ for all $x$, the function $f$ is convex upward on the entire real line $(- fty, \, \\infty)$. 5. Therefore: - (a) The curve of $f$ is convex upward in $(- fty, 0)$ is true. - (b) The function $f$ has an inflection point at $x=0$ is false because $f''(x)$ does not change sign. - (c) The curve of $f$ is convex upward in $(0, \, \\infty)$ is true. - (d) The function $f$ has no local maximum value is true because if $f$ is convex upward everywhere, it cannot have a local maximum. 6. Among the options, (a), (c), and (d) are true, but since the question asks which statement is true (singular), the best choice is (a) or (c). Both are correct, but typically the interval $(- fty, 0)$ is considered first. Final answer: (a) The curve of the function $f$ is convex upward in $(- fty, 0)$.