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AP EAMCET202023 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

If y = ( a x - b ) ( x - 1 ) ( x - 4 ) has a turning point P 2 , - 1 , then the values of a and b are

Options

  1. Aa = 0 ,   b = 1
  2. Ba = 1 ,   b = 0
  3. Ca = - 1 ,   b = 0
  4. Da = 0 ,   b = - 1

Correct answer

B. a = 1 ,   b = 0

Step-by-step solution

Given, y = a x - b x - 1 x - 4   … i has turning point P 2 , - 1 ∴ Point P satisfy the equation i ⇒ - 1 = 2 a - b 2 - 1 2 - 4 = 2 a - b - 2 ⇒ 2 a - b = 2   … ii As we know turning point of function is a point where f ' x = 0 . So, let's find d y d x From equation i , y x - 1 x - 4 = a x - b ⇒ y x 2 - 5 x + 4 = a x - b Differentiating the above equation w.r.t x ,   we get ⇒ y 2 x - 5 + x 2 - 5 x + 4 d y d x = a ⇒ d y d x = a - y 2 x - 5 x 2 - 5 x + 4

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