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BITSAT2009MathematicsApplication of DerivativesActual

The minimum value of the function (y=x^4-2 x^2+1 ) in the interval ( [ 1 2 , 2 ] ) is

Options

  1. A0
  2. B2
  3. C8
  4. D9

Correct answer

A. 0

Step-by-step solution

( dy dx = d dx ( x ^4-2 x ^2+1 )=4 x ( x ^2-1 ) ) For ( ). or ( , dy dx =0 ) (4 x ( x ^2-1 )=0 ; ), either ( x =0 ) or ( x = 1 ) (x=0 ) and (x=-1 ) does not belong to ( [ 1 2 , 2 ] ) ( d^2 y d x^2 =12 x^2-4 ( d^2 y d x^2 )_ x=1 ) (=12(1)^2-4=8 > 0 ) ( ) there is minimum value of function at ( x =1 ) ( ) minimum value is (y(1)=1^4-2(1)^2+1=1-2+1=0 )

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