Mathematics · JEE | CONTINUITY AND DIFFERENTIABILITY
हिन्दीGiven below are two statements: Statement I: If a function is differentiable at a point \( c \), then it is also continuous at that point. Statement II: The converse of the statement 'If a function is differentiable at a point, then it is continuous' is always true. In the light of the above statements, choose the most appropriate answer from the options given below:
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Correct answer · Option B
Statement I is correct but Statement II is incorrect.
Explanation
Every differentiable function is continuous (Theorem 3). However, the converse is false; continuous functions like \( f(x) = |x| \) are not differentiable at \( x = 0 \).