Question

Given the following statements about a function f: R → R, select the right option:

P: If f(x) is continuous at x = x₀, then it is also differentiable at x = x0.

Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.

R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.

1. P is true, Q is false, R is false
2. P is false, Q is true, R is true
3. P is false, Q is true, R is false
4. P is true, Q is false, R is true

Answer 1

Correct Answer - Option 2 : P is false, Q is true, R is true

The following properties are true in calculus:

• If a function is differentiable at any point, then it is necessarily continuous at the point.
• But the converse of this statement is not true i.e. continuity is a necessary but not sufficient condition for the Existence of a finite derivative.
• Differentiability implies Continuity. 
• Continuity does not necessarily imply differentiability.

 

Hence,

Statement P is wrong.

Statement Q is right. 

Statement R is right.