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NDA2018MathematicsContinuity and DifferentiabilityActual

Consider the function f ( x )= array cl x ^2 ( x ) & x 0 0 & x =0 array . . What is f ^ (0) equal to?

Options

  1. A0
  2. B1
  3. C–1
  4. DIt does not exist

Correct answer

A. 0

Step-by-step solution

aligned & f(x)= array cc x^2 n|x| & x 0 0 & x=0 array . & f^ (0)= _ h 0 f(h)-f(0) h & = _ h 0 h^2 |h|-0 h & = _ h 0 h n|h| & =0 aligned

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