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JEE Main2015MathematicsApplication of DerivativesActual

Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6 in 0 , 1 , respectively, then the ordered pair ( k , K ) is equal to:

Options

  1. A2 - 0.4 , 1
  2. B2 - 0.6 , 1
  3. C2 - 0.4 , 2 0.6
  4. D1,2 0.6

Correct answer

A. 2 - 0.4 , 1

Step-by-step solution

f x =   1 + x 0.6 1 + x 0.6 f ′ x =   0.6 1 + x - 0.4   1 + x 0.6 - 0.6   x 0.4 1 + x 0.6 1 + x 0.6 2 = 0.6   1 + x - 0.4   1 + x 0.6 - x - 0.4   1 + x 2 1 + x 0.6 2 = 0.6 x 0.4 - 1 1 + x 0.4 1 + x 0.6 2 Clearly it is always negative in [ 0 ,   1 ] minimum value would be at x = 1 . ( 1 + 1 ) 0.6 1 + 1 0.6 =   2 0.6 2 = 2 - 0.4 = k & maximum values would be at x = 0 ( 1 + 0 ) 0.6 1 + 0 0.6 = 1 1 = K Hence 2 - 0.4 , 1

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