The question asks for an analysis based on a graph. Specifically:

1. Part (a) asks to check all labeled points at which exactly two of the following are zero: $f(x)$, $f'(x)$, and $f''(x)$.
2. Part (b) asks to check all labeled points where both $f(x)$ and $f'(x)$ are nonzero and have the same sign.

Could you share the graph that this question references, or describe the points where features like zero-crossings, local maxima, minima, or inflection points occur? This information will help in determining where $f(x)$, $f'(x)$, and $f''(x)$ are zero or nonzero, and how their behavior relates at specific points.

Let me know if you would like further clarifications or explanations.