The graph you provided shows a function with distinct positive and negative intervals. To determine the positive and negative intervals:

1. The positive interval corresponds to the regions where the graph is above the x-axis, meaning the function values are greater than 0.
2. The negative interval corresponds to the regions where the graph is below the x-axis, meaning the function values are less than 0.

From the graph:

• The function is positive between the two x-intercepts: from $x = -1.38845$ to $x = 1.07363$.
• The function is negative on the interval where it is below the x-axis:
  • From $x = -\infty$ to $x \approx -1.38845$.
  • From $x \approx 1.07363$ to $x = \infty$.

Positive Intervals:

• $(-1.38845, 1.07363)$

Negative Intervals:

• $(-\infty, -1.38845)$
• $(1.07363, \infty)$

Would you like further analysis on this graph, such as finding the behavior near the x-intercepts or understanding the function's shape in more detail? Here are some additional questions for you:

1. How do we calculate the exact values of the intercepts from a given function?
2. What determines the concavity of the graph in this situation?
3. How do you find the local maxima and minima for this type of graph?
4. Can the graph be used to solve real-world problems? If so, how?
5. How do you use the first derivative to determine increasing and decreasing intervals?

Tip: Remember that a function is increasing when its derivative is positive and decreasing when its derivative is negative.