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NDA2013MathematicsContinuity and DifferentiabilityActual

A function f: R R is defined as f(x)=x^2 for x 0 and f(x)=-x for x 0 . Consider the following statements in respect of the above function: 1. The function is continuous at x=0 . 2. The function is differentiable at x=0 . Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

Test of continuity at x=0 R f(x)= _ x 0⁺ x^2=0 L f(x)= _ x 0⁻ (-x)=0 also, f(0)=(0)^2=0 Hence, f(x) is continuous at x=0 Differentiability f^ (x) for (x 0)=2 x f^ (0)=0f^ (x) for (x 0)=-1 f^ (0)=-1 Hence, f(x) is not differentiable at x=0 .

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