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AP EAMCET20227 Jul 2022Evening ShiftMathematicsContinuity and DifferentiabilityActual

Assertion (A) f(x)=|x| is differentiable at x=a 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.

Options

  1. AA is correct, R is correct, R is correct explanation of A
  2. BA is correct, R is correct, but R is not correct explanation of A .
  3. CA is correct, R is false
  4. DA is false, R is correct.

Correct answer

A. A is correct, R is correct, R is correct explanation of A

Step-by-step solution

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. f(x)=|x| is differentiable if x R- 0 .

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