The question asks on which intervals $\frac{dy}{dx} < 0$, meaning where the slope of the function $f(x)$ is negative (where the graph is decreasing).

Looking at the graph of $y = f(x)$:

1. In the interval $a < x < b$, the graph is increasing, so $\frac{dy}{dx} > 0$.
2. In the interval $b < x < c$, the graph is decreasing, so $\frac{dy}{dx} < 0$.
3. In the interval $c < x < d$, the graph is also decreasing, so $\frac{dy}{dx} < 0$.

Thus, $\frac{dy}{dx} < 0$ for intervals II ( $b < x < c$ ) and III ( $c < x < d$ ). Therefore, the correct answer is E) II and III.

Would you like more details or have any further questions?

Here are five follow-up questions for better understanding:

1. What does it mean when $\frac{dy}{dx} > 0$ or $\frac{dy}{dx} < 0$?
2. How do you identify the turning points on a graph?
3. What does the second derivative $\frac{d^2y}{dx^2}$ tell you about the graph's concavity?
4. Can a function be decreasing and still have $\frac{dy}{dx} = 0$ at some point?
5. How do critical points relate to increasing and decreasing intervals?

Tip: Always check both the slope and concavity of a graph to understand its behavior completely!