Question

Given the following statements about a function f: R $\to$ R, select the right option.

P : If f(x) is continuous at x = x${}_0$, then it is also differentiable at x = x${}_0$

Q : If f(x) is continuous at x = x${}_0$, then it may not be differentiable at x = x${}_0$.

R : If f(x) is differentiable at x = x${}_0$, then it is continuous at x = x${}_0$

• A. P is true, Q is false, R is false
• B. P is false, Q is true, R is true
• C. P is false, Q is true, R is false
• D. P is true, Q is false, R is true

Answer 1

The correct option is B P is false, Q is true, R is true

Continuity is the necessary condition for differentiability but it is not a sufficient condition.