To determine where $f'(x) > 0$, we need the following information:

1. The function $f'(x)$ (the derivative of $f(x)$) tells us where the original function $f(x)$ is increasing or decreasing.
2. When $f'(x) > 0$, $f(x)$ is increasing.
3. The intervals where $f'(x) > 0$ correspond to the regions where the derivative is positive.

Without the explicit function $f(x)$ or its derivative $f'(x)$, I can guide you through the process:

Step-by-step process:

1. Find the derivative $f'(x)$ (if not already given).
2. Set the inequality $f'(x) > 0$.
3. Solve the inequality to find the values of $x$ that make the derivative positive.
4. Identify the open intervals based on those values of $x$.

Choices:

• Option A: If there are open intervals where $f'(x) > 0$, select this option and input those intervals in interval notation.
• Option B: If there are no open intervals where $f'(x) > 0$, select this option.

To proceed further, I'd need the function $f(x)$ or its derivative $f'(x)$. Could you provide that, or do you have any additional information about the function?

Let me know if you need any clarifications or details. Here are 5 relevant questions that can help extend your understanding:

1. How do you compute the derivative of a given function $f(x)$?
2. What are the key points (critical points) of a function and how do they help in determining where $f'(x) > 0$?
3. What is the role of the second derivative $f''(x)$ in analyzing intervals of increasing and decreasing behavior?
4. How do you use a sign chart to determine where a derivative is positive or negative?
5. How can you solve inequalities involving the derivative to find intervals of increasing behavior?

Tip: Always check where the derivative equals zero or is undefined—these are critical points that could mark transitions between increasing and decreasing behavior.