### Home > CALC > Chapter 4 > Lesson 4.4.2 > Problem4-143

4-143.

The graph of $f^\prime(x)$ is shown below. Find the intervals where $f(x)$ is increasing, decreasing, concave up, and concave down.

We are looking at a graph of $f^\prime(x)$, but being asked about the graph of $f(x)$.
So think about what $f^\prime(x)$ tells us about $f(x)$.

If $f^\prime(x)$ is positive, then $f(x)$ is increasing (and vice versa).
If $f^\prime(x)$ is increasing, then $f(x)$ is concave up (and vise versa).