The negation of the statement "All continuous functions are differentiable."

  1. All continuous functions are not differentiable.
  2. Some continuous functions are differentiable.
  3. Some continuous functions are not differentiable.
  4. All differentiable functions are continuous

Answer (Detailed Solution Below)

Option 3 : Some continuous functions are not differentiable.
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AIIMS NORCET 8: Cardiovascular System
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Detailed Solution

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Calculation:

Always all differentiable functions are continuous. But all continuous functions are not differentiable.

So, the negation of the given statement is some continuous functions are not differentiable.

Hence, option (3) is correct.
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