Question

Assertion (A): If $ f(x) $ is not continuous at $ x = a $, then it is not differentiable at $ x = a $. Reason (R): If $ f(x) $ is differentiable at a point, then it is continuous at that point.

• (A) and (R) are both true, (R) is correct explanation of (A)
• (A) and (R) are both true, (R) is not correct explanation of (A)
• (A) is true, (R) is false
• (A) is false, (R) is true

Hint:

For a function to be differentiable at a point, it must be continuous at that point. Continuity is a necessary condition for differentiability.

Answer 1

The Correct Option is A

Assertion (A) states that if \( f(x) \) is not continuous at \( x = a \), then it is not differentiable at \( x = a \). This is true because for a function to be differentiable at a point, it must first be continuous at that point.
Reason (R) states that if \( f(x) \) is differentiable at a point, then it is continuous at that point. This is also true because differentiability implies continuity.
Thus, both assertion and reason are true, and reason correctly explains the assertion.