Consider the following statements:
1. The derivative where the function attains maxima or minima be zero.
2. If a function is differentiable at a point, then it must be continuous at that point.
Which of the above statements is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To solve the question, we need to analyze the two statements provided:

1. **Statement 1**: The derivative where the function attains maxima or minima is zero.
2. **Statement 2**: If a function is differentiable at a point, then it must be continuous at that point.

### Step 1: Analyze Statement 1
- A function \( f(x) \) attains a maximum or minimum at a point \( x = c \) if the derivative \( f'(c) = 0 \). This is known as the first derivative test.
- However, it is important to note that while \( f'(c) = 0 \) indicates a critical point, not all critical points are necessarily maxima or minima. A critical point could also be a point of inflection where the function does not attain a maximum or minimum.
- Therefore, while it is true that at a maximum or minimum the derivative is often zero, it is not a definitive condition. Hence, this statement is **not always true**.

### Conclusion for Statement 1:
- **Statement 1 is False.**

### Step 2: Analyze Statement 2
- A function \( f(x) \) is said to be differentiable at a point \( x = c \) if the derivative \( f'(c) \) exists.
- A fundamental theorem in calculus states that if a function is differentiable at a point, then it must also be continuous at that point. This means that differentiability implies continuity.
- Therefore, if \( f \) is differentiable at \( c \), it guarantees that \( f \) is continuous at \( c \).

### Conclusion for Statement 2:
- **Statement 2 is True.**

### Final Conclusion:
- Among the two statements, only **Statement 2 is correct**.

### Summary of Answers:
- Statement 1: False
- Statement 2: True
- Therefore, the correct answer is that only Statement 2 is correct.

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