Problem

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.

Solution

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 :\(\boxed{1. \: f A \: 2. \: f^{\prime} B \: 3. \: f^{\prime \prime} C}\)

From Solvely APP
Source: https://solvelyapp.com/problems/15310/

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