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AP EAMCET2011MathematicsContinuity and Differentiability

If f(x)=|x|+| x| for x (- 2 , 2 ) , then its left hand derivative at x=0 is

Options

  1. A0
  2. B-1
  3. C-2
  4. D-3

Correct answer

C. -2

Step-by-step solution

aligned & f(x)=|x|+| x| & LHD = _ h 0 f(0-h)-f(0) 0-h & = _ h 0 |0-h|+| (0-h)|-(0+0) 0-h & = _ h 0 h+ h -h =- _ h 0 (1+ h h ) & =-(1+1)=-2 aligned

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