To solve this problem, we need to determine the x-values where the graphs have relative minima or maxima by examining the turning points of each polynomial graph.

Analyzing the Graphs

Graph 9:

1. Relative Minima: A relative minimum occurs where the graph changes from decreasing to increasing.

   • The graph shows a relative minimum at $x = 2$ and another at $x = 7$.

2. Relative Maxima: A relative maximum occurs where the graph changes from increasing to decreasing.

   • The graph shows a relative maximum at $x = 5$.

Graph 10:

1. Relative Minima:

   • The graph shows a relative minimum at $x = 1$.

2. Relative Maxima:

   • The graph shows a relative maximum at $x = -2$ and another at $x = 4$.

Answers:

• Graph 9:

  • Relative minimums at $x = 2, 7$
  • Relative maximums at $x = 5$

• Graph 10:

  • Relative minimums at $x = 1$
  • Relative maximums at $x = -2, 4$

Would you like further details or explanations? Here are some related questions that might help you understand the topic better:

1. What defines a relative minimum or maximum in a polynomial graph?
2. How can you determine the relative extrema by looking at the derivative of a function?
3. Why do polynomial functions have relative extrema?
4. Can a polynomial of degree 3 have more than two relative extrema?
5. How does the degree of a polynomial affect the number of turning points?

Tip: When analyzing graphs, remember that the relative extrema occur where the slope of the function changes sign, indicating a turning point.