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The image contains two sections labeled "What's More" and "What I Have Learned," focusing on mathematical problems and concepts.

### "What's More" Section:
This section presents a math problem where you are asked to identify which of the given options correspond to the **critical numbers** of a function. The problem provides a function and asks to solve for critical numbers.

### "What I Have Learned" Section:
This section includes fill-in-the-blank statements related to solving inequalities, particularly focusing on concepts like **extraneous solutions**, **critical values**, and **solving rational inequalities**.

### Let's break down each section:

1. **Critical Numbers**:
   - Critical numbers of a function are the values of \( x \) where the derivative \( f'(x) \) is zero or undefined.
   - You need to solve the derivative \( f'(x) \) to find where it equals zero or is undefined.

2. **Key Concepts to Learn**:
   - **Extraneous Solutions**: Solutions obtained from the process that do not satisfy the original equation.
   - **Critical Values**: Values of \( x \) where the expression is equal to zero or undefined, crucial for solving inequalities.
   - **First Step in Solving Rational Inequalities**: Set the inequality to zero and find the critical values.

### Would you like to solve the specific problems or get detailed explanations on the concepts?

#### Here are 5 related questions for further practice:
1. How do you calculate the derivative of a given function?
2. What is the process for identifying extraneous solutions in an equation?
3. How do you solve inequalities that involve rational functions?
4. What is the significance of critical points in determining the behavior of a function?
5. How can you verify whether a critical number is a maximum, minimum, or a point of inflection?

**Tip:** When solving for critical points, always check if they lie within the domain of the function to ensure they are valid solutions.

What are the critical numbers of a function and how are they used in solving rational inequalities? What are extraneous solutions and critical values?

Explore how to identify critical numbers of a function and solve rational inequalities. Understand the concept of extraneous solutions and critical values with step-by-step explanations, ideal for high school students.

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