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JEE Main2005MathematicsApplication of DerivativesActual

If f is a real-valued differentiable function satisfying |f(x)-f(y)| (x-y)^2, x, y R and f(0)=0 , then f(1) equals

Options

  1. A-1
  2. B0
  3. C2
  4. D1

Correct answer

B. 0

Step-by-step solution

aligned & f^ (x)= _ h 0 f(x+h)-f(x) h & |f^ (x) |= _ h 0 | f(x+h)-f(x) h | _ h 0 | (h)^2 h | & |f^ (x) | 0 f^ (x)=0 f(x)= constant & As f(0)=0 f(1)=0 . aligned

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