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BITSAT2011MathematicsApplication of DerivativesActual

The minimum value of (f(x)= ^4 x+ ^4 x ) in the interval ( (0, 2 ) ) is

Options

  1. A( 1 2 )
  2. B2
  3. C( 2 )
  4. D1

Correct answer

A. ( 1 2 )

Step-by-step solution

Let (y= ^4 x+ ^4 x ) ( aligned & d y d x =4 ^3 x x+4 ^3 x(- x) & =4 x cox ( ^2 x- ^2 x ) & =(2 2 x)(- 2 x)=- 4 x & d y d x =0 4 x=0 4 x=0, , 2 , 3 aligned ) or ( x =0, 4 , 2 , 3 4 , , x = 4 )

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