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The open intervals on which f is increasing. (Enter your answer using interval notation.)

To determine the open intervals on which the function \( f(x) \) is increasing, we need to identify the regions where the slope of the curve is positive (i.e., where the graph is moving upward from left to right).

From the graph provided, the function increases in the following intervals:

1. From \( x = -\infty \) up to the first turning point, which is roughly at \( x \approx 0.3 \).
2. From the next local minimum, around \( x \approx 1.7 \), until the graph continues to rise indefinitely.

Thus, the function \( f(x) \) is increasing on the following intervals:

\[
(-\infty, 0.3) \cup (1.7, \infty)
\]

Would you like further explanation, or do you have any questions?

Here are five related questions you might find helpful:
1. How can you find the intervals where a function is decreasing?
2. What is the significance of local minima and maxima for identifying intervals of increase or decrease?
3. How do the first and second derivatives relate to the intervals where a function is increasing?
4. Can a function be increasing or decreasing at a single point, like a critical point?
5. What does it mean when a function is constant over an interval?

**Tip:** Remember, a function is increasing when the derivative \( f'(x) > 0 \) and decreasing when \( f'(x) < 0 \).

The open intervals on which f is increasing.

Learn how to find the increasing intervals of a function by analyzing its graph. This problem focuses on key calculus concepts like critical points and the first derivative test. Suitable for students in Grades 10-12.

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