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AP EAMCET202318 May 2023Morning ShiftMathematicsApplication of DerivativesActual

Let : R R be a differentiable function such that | f ( x )- f (4)| 2| x - y |^ 3 2 x , y R If f(0)=1 , then ₀^1 f^2(x) d x=

Options

  1. A-2
  2. B1 2
  3. C0
  4. D1

Correct answer

D. 1

Step-by-step solution

|f(x)-f(y)| 2|x-y|^ 3 / 2 | f(x)-f(y) x-y | 2|x-y|^ 1 2 as x y , we get : | f ^ ( y ) | 0 | f ^ ( y ) |=0 absolute value can not be negative aligned & f^ (y)=0 & f(y)=c aligned f(0)=1 1=c f ( y )=1 Now, ₀^1 f ^2( x ) dx = ₀^1 1 dx =1-0=1

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