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NEST2018MathematicsContinuity and Differentiability

Let f, g: R R be such that f(x)=x^k g(x) where k is a positive integer. Suppose g is continuous at x=0 . Then

Options

  1. Af is continuous at x=0 but not differentiable at x=0
  2. Bf is differentiable at x=0
  3. Cf^ (0)=0 for every positive integer k
  4. Df^ (0)=g(0) if k=1 and f^ (0)=0 if k 2

Correct answer

D. f^ (0)=g(0) if k=1 and f^ (0)=0 if k 2

Step-by-step solution

No solution available.

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