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The image contains a mathematical question written in Vietnamese. Here's the translated problem and the available options:

**Problem** (Câu 12): Given the function \( y = 3x^4 - 6x^2 + 1 \), which of the following conclusions is correct?

**Options**:
- A. \( y_{CD} = -2 \)
- B. \( y_{CD} = 1 \)
- C. \( y_{CD} = -1 \)
- D. \( y_{CD} = 2 \)

This question seems to be asking about critical values (possibly local extrema or specific points like minimum or maximum values) of the function \( y = 3x^4 - 6x^2 + 1 \).

### Solution Process:
1. **Find the derivative** of the function to locate critical points:
   \[
   y' = \frac{d}{dx} \left( 3x^4 - 6x^2 + 1 \right) = 12x^3 - 12x
   \]
2. **Set the derivative equal to 0** to find critical points:
   \[
   12x^3 - 12x = 0 \quad \Rightarrow \quad 12x(x^2 - 1) = 0
   \]
   Solving this:
   \[
   x = 0, \quad x = 1, \quad x = -1
   \]
3. **Substitute these critical points into the original function** to find the corresponding \( y \) values (i.e., \( y_{CD} \)):
   - For \( x = 0 \): 
     \[
     y(0) = 3(0)^4 - 6(0)^2 + 1 = 1
     \]
   - For \( x = 1 \): 
     \[
     y(1) = 3(1)^4 - 6(1)^2 + 1 = 3 - 6 + 1 = -2
     \]
   - For \( x = -1 \): 
     \[
     y(-1) = 3(-1)^4 - 6(-1)^2 + 1 = 3 - 6 + 1 = -2
     \]

Thus, the critical values of \( y \) are \( 1 \) at \( x = 0 \), and \( -2 \) at \( x = 1 \) and \( x = -1 \).

### Correct Conclusion:
The correct option is **B. \( y_{CD} = 1 \)**, since at \( x = 0 \), the value of \( y \) is 1.

Let me know if you'd like further details or explanations!

### Related Questions:
1. How do you determine local extrema using the second derivative?
2. What is the significance of critical points in determining the shape of a graph?
3. Can a function have more than one local maximum or minimum?
4. How do higher-degree polynomials typically behave as \( x \to \infty \) or \( x \to -\infty \)?
5. How would you sketch the graph of \( y = 3x^4 - 6x^2 + 1 \)?

### Tip:
Always check the second derivative to confirm if a critical point is a local maximum, minimum, or inflection point!

Câu 12: Cho hàm số y = 3x^4 - 6x^2 + 1. Kết luận nào sau đây là đúng? A. y_CD = -2, B. y_CD = 1, C. y_CD = -1, D. y_CD = 2

This problem asks students to determine critical points of the polynomial y = 3x^4 - 6x^2 + 1 and identify the correct critical value from given options. It involves calculus concepts like finding the derivative and solving for critical points. Suitable for Grades 11-12.

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