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

Options

A. Only I
B. Only II
C. Both I and II
D. Neither I nor II

Answer

To analyze the given statements, we will evaluate each one step by step.

### Step 1: Evaluate Statement I
**Statement I:** The derivative where the function attains maxima or minima is zero.

1. **Understanding Maxima and Minima:**
- A function \( f(x) \) attains a maximum or minimum at a point \( x = c \) if the slope of the tangent line at that point is zero. This is because at these points, the function does not increase or decrease, hence the derivative \( f'(c) = 0 \).

2. **Conclusion for Statement I:**
- Therefore, Statement I is **correct** because the derivative at points of maxima or minima is indeed zero.

### Step 2: Evaluate Statement II
**Statement II:** If a function is differentiable at a point, then it must be continuous at that point.

1. **Understanding Differentiability and Continuity:**
- A function \( f(x) \) is said to be differentiable at a point \( x = c \) if the derivative \( f'(c) \) exists. For the derivative to exist, the function must be continuous at that point.
- If a function is not continuous at \( x = c \), it cannot have a well-defined tangent (slope), and thus the derivative cannot exist.

2. **Conclusion for Statement II:**
- Therefore, Statement II is also **correct** because differentiability implies continuity.

### Final Conclusion
Both statements I and II are correct.

### Summary of the Solution:
- Statement I is correct: The derivative at maxima or minima is zero.
- Statement II is correct: If a function is differentiable at a point, it must be continuous at that point.