To determine where $f'(x) < 0$, we need to look at the graph of $f(x)$ and identify the intervals where the function is decreasing, since the derivative $f'(x)$ is negative during those intervals.

Looking at the graph:

• From point $a$ to $b$, the graph is decreasing, so $f'(x) < 0$.
• From point $c$ to $e$, the graph is decreasing, so $f'(x) < 0$.
• From point $f$ to $g$, the graph is decreasing, so $f'(x) < 0$.

Thus, the intervals where $f'(x) < 0$ are $(a, b)$, $(c, e)$, and $(f, g)$.

Therefore, the correct answer is:

B. (a, b), (c, e), (f, g).

Would you like further explanation on how to analyze such graphs or any other details?

Here are 5 follow-up questions you might find helpful:

1. How do you identify where $f'(x) > 0$ on a graph?
2. What happens to the graph of $f(x)$ at points where $f'(x) = 0$?
3. Can a graph have sections where $f'(x) = 0$ and still be decreasing or increasing elsewhere?
4. How would concavity affect the intervals where $f'(x) < 0$?
5. What is the significance of inflection points in determining the behavior of $f'(x)$?

Tip: Always remember that a function is decreasing when its derivative is negative, and increasing when its derivative is positive.