Contrapositive of the statement :
'If a function f is differentiable at a, then it is also continuous at a', is:
'If a function f is differentiable at a, then it is also continuous at a', is:
Show Hint
- If a function f is continuous at a, then it is not differentiable at a.
- If a function f is not continuous at a, then it is differentiable at a.
- If a function f is not continuous at a, then it is not differentiable at a.
- If a function f is continuous at a, then it is differentiable at a.
The Correct Option is C
Solution and Explanation
The statement is \(p \Rightarrow q\). Its contrapositive is \(\sim q \Rightarrow \sim p\).
\(\sim q\): f is not continuous at a; \(\sim p\): f is not differentiable at a.
So the contrapositive is: if f is not continuous at a, then it is not differentiable at a.
Answer: (3) If a function f is not continuous at a, then it is not differentiable at a.
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