The graph of a function f is given. Use the graph to find each of the following. a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima? a. Find the numbers, if any, at which f has a relative maximum, and find the relative maxima(maximum). Select the corre to complete your choice. A. The function $$ f $$ has (a) relative maxima(maximum) at (Use a comma to separate answers as needed.) B. The function f has no relative maxima. b. Find the numbers, if any, at which f has a relative minimum, and find the relative minima(minimum). Select the corre complete your choice.

Question

UpStudy AI · Accepted Answer

To solve this problem, we need to analyze the graph of the function $$ f $$ to identify the points where it has relative maxima and minima. Since I don't have access to the graph, I will guide you through the steps you would take to find these points.

### Step-by-Step Guide

1. **Identify Critical Points:**
   - Look for points on the graph where the slope of the function changes from positive to negative (potential relative maxima) or from negative to positive (potential relative minima).
   - These points are often where the derivative $$ f'(x) = 0 $$ or where $$ f'(x) $$ is undefined.

2. **Determine Relative Maxima:**
   - For each critical point identified, check the values of $$ f $$ at those points.
   - A relative maximum occurs at a point $$ x = c $$ if $$ f(c) $$ is greater than the values of $$ f $$ at points immediately to the left and right of $$ c $$.
   - List the $$ x $$-values where these maxima occur and their corresponding $$ f(x) $$ values.

3. **Determine Relative Minima:**
   - Similarly, check the values of $$ f $$ at the critical points for relative minima.
   - A relative minimum occurs at a point $$ x = c $$ if $$ f(c) $$ is less than the values of $$ f $$ at points immediately to the left and right of $$ c $$.
   - List the $$ x $$-values where these minima occur and their corresponding $$ f(x) $$ values.

### Example Format for Answers

- **For Relative Maxima:**
  - If you find that $$ f $$ has relative maxima at $$ x = a $$ and $$ x = b $$ with maximum values $$ f(a) $$ and $$ f(b) $$, you would write:
    - A. The function $$ f $$ has relative maxima at $$ a, b $$ (with corresponding maximum values $$ f(a), f(b) $$).
  - If there are no relative maxima, you would write:
    - B. The function $$ f $$ has no relative maxima.

- **For Relative Minima:**
  - If you find that $$ f $$ has relative minima at $$ x = c $$ and $$ x = d $$ with minimum values $$ f(c) $$ and $$ f(d) $$, you would write:
    - A. The function $$ f $$ has relative minima at $$ c, d $$ (with corresponding minimum values $$ f(c), f(d) $$).
  - If there are no relative minima, you would write:
    - B. The function $$ f $$ has no relative minima.

### Conclusion

Once you analyze the graph and identify the critical points, you can fill in the answers based on your findings. If you have specific points or values from the graph, please provide them, and I can help you format the final answers accordingly.
To find the relative maxima and minima of the function $$ f $$, follow these steps: 1. **Identify Critical Points:** Look for points where the slope changes (where $$ f'(x) = 0 $$ or is undefined). 2. **Determine Maxima:** Find points where $$ f(x) $$ is higher than nearby points. 3. **Determine Minima:** Find points where $$ f(x) $$ is lower than nearby points. **Example Answers:** - **Relative Maxima:** If $$ f $$ has maxima at $$ x = a $$ and $$ x = b $$, write: - A. The function $$ f $$ has relative maxima at $$ a, b $$ (with corresponding maximum values $$ f(a), f(b) $$). - **Relative Minima:** If $$ f $$ has minima at $$ x = c $$ and $$ x = d $$, write: - A. The function $$ f $$ has relative minima at $$ c, d $$ (with corresponding minimum values $$ f(c), f(d) $$). If there are no maxima or minima, select the appropriate option accordingly.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Calculus Questions