Answer
Graph B represents $f(x)$ and graph A represents $f'(x)$.
Work Step by Step
As the derivative $f'(x)$ represents the change in the form of the function $f(x)$, examining the graph of $f'(x)$ shows clues about the graph of $f(x)$.
Looking at these two graphs, we notice the followings:
- The area where graph A is positive, graph B is increasing; and where graph A is negative, graph B is decreasing. We know that the sign of $f'(x)$ represents whether $f(x)$ is rising or falling.
- Graph A reaches $0$ where graph B changes direction and appears to have a horizontal tangent. It is also known that $f(x)$ has a horizontal tangent where $f'(x)=0$.
We therefore can conclude that graph B represents $f(x)$ while graph A represents $f'(x)$.
