https://file.aiquickdraw.com/mathbot/file/1727043481256sdyi08vz.jpg

From the image, it looks like a calculus problem asking for relative extrema (minima and maxima) based on the graph of \( y = f(x) \). The graph shows critical points where the function changes direction, allowing us to determine the relative minima and maxima.

### a. Identifying the relative minima:
- Based on the graph, we can see **two relative minima**.
  1. The first minimum occurs at \( x = -6 \) with a value of \( y = -5 \).
  2. The second minimum occurs at \( x = 5 \) with a value of \( y = 4 \).

So, the answer to part (a) is:
- Leftmost minimum value: \( -5 \) occurring at \( x = -6 \).
- Rightmost minimum value: \( 4 \) occurring at \( x = 5 \).

### b. Identifying the relative maxima:
- From the graph, there is **only one relative maximum**, which occurs at \( x = 0 \), and the maximum value is \( y = -0.5 \).

So, the answer to part (b) is:
- Maximum value: \( -0.5 \) occurring at \( x = 0 \).

### Answers:
- Part (a): Two minima.
  - Leftmost minimum value: \( -5 \), occurring at \( x = -6 \).
  - Rightmost minimum value: \( 4 \), occurring at \( x = 5 \).
- Part (b): One maximum.
  - Maximum value: \( -0.5 \), occurring at \( x = 0 \).

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Would you like further clarification or details on any part of this solution?

Here are 5 questions that may expand your understanding:
1. What is the difference between relative and absolute extrema?
2. How can we find relative extrema using derivatives instead of the graph?
3. Why does a change in the direction of the graph indicate an extremum?
4. How would you determine if a point is a minimum or maximum using the second derivative test?
5. Can a function have multiple maxima and minima in a given interval?

**Tip:** When analyzing a function graph, the x-values where the slope changes sign (from positive to negative or vice versa) indicate potential maxima or minima points.

Use the graph of y = f(x) to answer the questions. Complete parts a and b.

This problem involves identifying the relative minima and maxima from the graph of y = f(x). By analyzing the turning points on the graph, we determine that there are two relative minima and one relative maximum. Learn how to use graph analysis to solve this problem in calculus.

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