Assertion (A) : A continuous function is always differentiable.
Reason (R ) : A differentiable function is always continuous.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Answer

To determine the validity of the assertion and reason provided in the question, we can analyze them step by step.

### Step 1: Understanding the Assertion (A)
The assertion states: "A continuous function is always differentiable."

- **Analysis**: This statement is not true. A function can be continuous at a point but not differentiable at that point. A classic example is the function \( f(x) = |x| \). This function is continuous everywhere, but it is not differentiable at \( x = 0 \) because it has a sharp point (or cusp) at that location.

### Step 2: Understanding the Reason (R)
The reason states: "A differentiable function is always continuous."

- **Analysis**: This statement is true. If a function is differentiable at a point, it means that the derivative exists at that point, which implies that the function must be continuous at that point. The existence of the derivative requires the function to not have any breaks, jumps, or points of discontinuity.

### Step 3: Conclusion
Now, we can conclude the truth values of the assertion and reason:

- **Assertion (A)**: False (A continuous function is not always differentiable)
- **Reason (R)**: True (A differentiable function is always continuous)

### Final Answer
Therefore, the assertion is false, and the reason is true.