AP EAMCET · Maths · Continuity and Differentiability
Assertion (A) \(f(x)=|x|\) is differentiable at \(x=a \neq 0\) and continuous but not differentiable at \(x=0\)
Reason (R) If a function is differentiable at a point, then it is continuous at the point. But converse is not true.
- A \(\mathrm{A}\) is correct, \(\mathrm{R}\) is correct, \(\mathrm{R}\) is correct explanation of \(\mathrm{A}\)
- B A is correct, \(\mathrm{R}\) is correct, but \(\mathrm{R}\) is not correct explanation of \(\mathrm{A}\).
- C \(\mathrm{A}\) is correct, \(\mathrm{R}\) is false
- D A is false, \(R\) is correct.
Answer & Solution
Correct Answer
(A) \(\mathrm{A}\) is correct, \(\mathrm{R}\) is correct, \(\mathrm{R}\) is correct explanation of \(\mathrm{A}\)
Step-by-step Solution
Detailed explanation
From the graph of \(f(x)=|x|\), it is clear that \(f(x)\) is everywhere continuous but not differentiable at \(x=0\), due to sharp edge. \(\therefore f(x)=|x|\) is differentiable if \(x \in R-\{0\}\).
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