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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!

The graph of y = f(x) is given. On which intervals is dy/dx < 0?

Understand how to determine the intervals where a function is decreasing by analyzing its derivative. This calculus problem focuses on identifying where dy/dx < 0 on a graph of y = f(x). Suitable for high school students in Grades 10-12.

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