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BITSAT2012MathematicsApplication of DerivativesActual

If f(x)=x^ x and f(0)=0, then the value of for which Rolle's theorem can be applied in [0,1] is

Options

  1. A-2
  2. B-1
  3. C0
  4. D1 / 2

Correct answer

D. 1 / 2

Step-by-step solution

For Rolle's theorem in [ a , b ], f ( a )= f ( b ), In [0,1] f (0)= f (1)=0 the function has to be continuous in [0,1] f(0)= _ x 0⁺ f(x)=0 _ x 0 x^ x=0 _ x 0 x x^ - =0 Applying L.H. Rule _ x 0 1 / x - x^ - -1 =0 _ x 0 -x^ =0 >0

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