The diagram shows the graph of the curve $y = f(x)$ - HSC - SSCE Mathematics Extension 2 - Question 8 - 2018 - Paper 1

To determine the values of $x$ where the concavity of the curve changes, we need to analyze the second derivative of $F(x)$. The concavity changes at points where the second derivative changes sign.

1. Find First Derivative: The first derivative of $F(x)$ is given by the Fundamental Theorem of Calculus: $F'(x) = f(x)$.

2. Find Second Derivative: The second derivative is: $F''(x) = f'(x)$.

3. Determine Concavity Changes: The points of inflection, where the concavity changes, are values of $x$ where $F''(x) = f'(x) = 0$. From the graph, it can be observed that $f(x)$ changes from concave up to concave down at the points $a$ and $c$, and it is a critical point at $d$ due to the behavior of $f(x)$ (i.e., $f'(d)=0$ as indicated by a local extremum).

Thus, the concavity changes at the values: a, c, d. The correct answer is B. a, c.