The problem is asking to determine which of the labeled points (A, B, C, D) are inflection points of the function $f(x)$, based on the graph of $f(x)$.

Key concept:

An inflection point occurs where the second derivative of the function, $f''(x)$, changes sign. This typically corresponds to points where the concavity of the graph transitions from concave up to concave down, or vice versa.

Observations:

1. At points $A$ and $D$, the graph is concave up (parabolic shape).
2. At points $B$ and $C$, the graph transitions between concave up and concave down. This is indicated by the change in the curvature of the graph.

Thus, $B$ and $C$ are the inflection points, as they mark where $f''(x) = 0$ and the concavity changes.

Final Answer:

The inflection points of the graph are $\mathbf{B}$ and $\mathbf{C}$.

Would you like a detailed explanation of second derivatives and inflection points, or have any questions about this concept?

Related Questions:

1. What is the mathematical process to find inflection points using derivatives?
2. How does the concavity of a function relate to its second derivative?
3. Can there be an inflection point if $f''(x) = 0$ but the concavity does not change?
4. How can we identify inflection points from a function's equation instead of its graph?
5. What are practical applications of finding inflection points in real-world scenarios?

Tip:

When analyzing graphs, always look for changes in curvature to identify inflection points.