From the image you provided, we can analyze the function based on the graph and identify key features like relative maxima, minima, and the intervals of increasing and decreasing behavior.

Analyzing the Graph:

1. Relative Maximum and Minimum:

   • A relative maximum is the highest point in a particular region of the graph.
   • From the graph, it appears there is a peak at point $(5, 1)$, indicating that there is a relative maximum at $x = 5$ with a value of 1.

2. Intervals of Increasing and Decreasing:

   • The function increases from left to right until it reaches the peak at $(5, 1)$. This means the function is increasing on the interval approximately $(-3, 5)$.
   • After reaching the maximum at $x = 5$, the function decreases. This means the function is decreasing on the interval approximately $(5, 8)$.

Summary of Answers:

• Relative Maximum:
  • Value: 1
  • At $x = 5$

Would you like more detailed explanations or have any questions about this analysis?

5 Related Questions:

1. How can we find relative maxima and minima using calculus?
2. What is the difference between absolute maximum and relative maximum?
3. How do the first and second derivatives relate to finding maxima and minima?
4. What are the conditions under which a function is increasing or decreasing?
5. How can you determine concavity and inflection points from a graph?

Tip: To determine increasing and decreasing intervals, look at the slope of the function in different regions. Where the slope is positive, the function is increasing; where it's negative, the function is decreasing.