Question

Contrapositive of the statement : ‘If a function $f$ is differentiable at $a$, then it is also continuous at $a$’ , is:

• A. If a function $f$ is not continuous at $a$, then it is not differentiable at $a$.
• B. If a function $f$ is continuous at $a$, then it is differentiable at $a$.
• C. If a function $f$ is continuous at $a$, then it is not differentiable at $a$.
• D. If a function $f$ is not continuous at $a$, then it is differentiable at $a$.

Answer 1

The correct option is A

If a function $f$ is not continuous at $a$, then it is not differentiable at $a$.

Explanation for correct option:

Step-1:Expressing the given data.

‘If a function $f$ is differentiable at $a$, then it is also continuous at $a$’

Let $P=$function $f$ is differentiable at ‘$a$’

$Q=$function $f$ is continuous at ‘$a$’

Step-2: Finding contrapositive of the given statement.

Given, $P\to Q$

Contrapositive is $~Q\to ~P$

Therefore, contrapositive statement is ‘’If a function $f$ is not continuous at $a$, then it is not differentiable at $a$''

Hence, correct answer is option $\left(A\right)$