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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let f(x)=(x+|x|)|x| , then for all x

Options

  1. Af is continuous
  2. Bf^ is differentiable x R
  3. Cf^ is continuous
  4. Df^ is continuous

Correct answer

C. f^ is continuous

Step-by-step solution

f(x)= cases (x-x)(-x)=0 & ; x 0 (x+x) x=2 x^2 & ; x 0 cases f is continuous and differentiable f^ (x) is continuous but not differentiable at x=0

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