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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = cases x^n 1 x & , x 0 0 & , x = 0 cases Such that f(x) is continuous at x = 0 ; f'(0) is real and finite; and _ x 0 f'(x) does not exist. This holds true for which of the following values of n ?

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

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