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AP EAMCET202119 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The stationary points of the curve y = 8 x 2 - x 4 - 4 are____

Options

  1. A( 0 , − 4 ) , ( 2 , 12 ) , ( − 2 , 12 )
  2. B( 0 , 4 ) , ( − 2 , 12 ) , ( 1 , 2 )
  3. C( 0 , − 4 ) , ( − 1 , 2 ) , ( 2 , 12 )
  4. D( 0 , 4 ) , ( − 1 , 2 ) , ( 1 , 2 )

Correct answer

A. ( 0 , − 4 ) , ( 2 , 12 ) , ( − 2 , 12 )

Step-by-step solution

Given curve y   =   8 x 2   -   x 4   - 4 Differentiate on both sides d y d x   =   16 x   -   4 x 3 To get stationary points d y d x   =   0 4 x 4 - x 2 = 0 ⇒ x   =   0   ,   x 2   =   4 ⇒   x   =   0   ,   ± 2 x =   0   ⇒ y   =   8 0 - 0 - 4 = - 4 x   =   2   ⇒   y   =   8 4   -   16   -   4   =  

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