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AP EAMCET202119 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

For which value(s) of ' a ' , f ( x ) = - x 3 + 4 a x 2 + 2 x - 5 is decreasing for every ' x ' ?

Options

  1. A1 , 2
  2. B3 , 4
  3. CR
  4. DNo value of ' a '

Correct answer

D. No value of ' a '

Step-by-step solution

Given that f x   =   - x 3   +   4 a x 2   +   2 x   -   5 Differentiation on both sides f ' x   =   - 3 x 2   +   8 a x   + 2 Given that function is decreasing ⇒ f ' x   <   0 ⇒ - 3 x 2 + 8 a x + 2   < 0 If A x 2 + B x + C   <   0   ⇒   A   <   0 ,   ∆   =   B 2   -   4 A C   < 0 Here Discriminant ∆   =   64 a

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