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The problem appears to involve contour lines of a function \( f(x, y) \), where we are asked to evaluate the correctness of two statements regarding points \( L \), \( M \), and \( N \) on these contours.

### Explanation:
1. **Contour Lines**: These are curves along which the function \( f(x, y) \) takes a constant value. So, for any point on a specific contour line, the value of \( f(x, y) \) is the same.

2. **Observations from the Graph**:
   - Points \( L \) and \( M \) lie on the same contour line.
   - Point \( N \) lies on a different contour, which is further down from the one containing \( L \) and \( M \).
   - Since contour lines represent constant function values, this means:
     \[
     f(L) = f(M) \quad \text{(since they are on the same contour line)},
     \]
     but \( f(N) \) is different from \( f(L) \) and \( f(M) \) because it is on a different contour.

### Analyzing the Statements:
- **Statement 1**: \( f(L) = f(M) = f(N) \).  
  This statement is **incorrect** because \( f(N) \) is on a different contour, so its value differs from \( f(L) \) and \( f(M) \).
  
- **Statement 2**: \( f(L) = f(M) \neq f(N) \).  
  This statement is **correct**, as \( L \) and \( M \) are on the same contour, but \( N \) is on a different contour with a different function value.

### Correct Answer:
The correct choice is **ב (2)**, meaning only statement 2 is correct.

Would you like further details or clarifications?

Here are five related questions to deepen understanding:
1. What does it mean when points lie on the same contour line?
2. How do you determine the direction of the gradient relative to the contour lines?
3. What is the relationship between contour lines and level curves?
4. How do the values of a function change as you move between different contour lines?
5. How can contour plots be used in optimization problems?

**Tip**: Contour plots are useful for visualizing multivariable functions, where each contour represents all points with the same function value.

The problem presents two contour lines of the function f(x, y) and asks to evaluate the correctness of two statements involving points L, M, and N on these contours. Statement 1 claims f(L) = f(M) = f(N), and Statement 2 claims f(L) = f(M) != f(N). The task is to identify the correct statement.

This problem involves analyzing contour lines of a multivariable function f(x, y). The goal is to determine the correctness of two statements about points L, M, and N lying on different contour lines. A step-by-step solution explains the relationship between points on the same and different contours.

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