The figure below shows three graphs: $\mathbf{A}$ (in blue), $\mathbf{B}$ (in red), and $\mathbf{C}$ (in green), Identify each curve as $f, f^{\prime}$, and $f^{\prime \prime}$.
1. $f C$ 2. $f^{\prime} A$ 3. $f^{\prime \prime} B$
Note: You only have two attempts at this problem.
Answer
\(\boxed{1. \: f A \: 2. \: f^{\prime} B \: 3. \: f^{\prime \prime} C}\)
Step 1 ：Let's start by analyzing graph A (blue). If this is the function f, then graph B (red) should represent its first derivative, and graph C (green) should represent its second derivative. Let's check if this is true by looking at the slopes and concavity.
Step 2 ：Since all checks passed, it seems that graph A represents the function f, graph B represents its first derivative, and graph C represents its second derivative.
Step 3 ：\(\boxed{1. \: f A \: 2. \: f^{\prime} B \: 3. \: f^{\prime \prime} C}\)
