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JEE Main202125 Feb 2021Morning ShiftMathematicsApplication of DerivativesActual

If Rolle's theorem holds for the function f x = x 3 - a x 2 + b x - 4 , x ∈ 1 , 2 with f ' 4 3 = 0 , then ordered pair a , b is equal to :

Options

  1. A- 5 , - 8
  2. B- 5 , 8
  3. C5 , 8
  4. D5 , - 8

Correct answer

C. 5 , 8

Step-by-step solution

f 1 = f 2 ⇒   1 - a + b - 4 = 8 - 4 a + 2 b - 4 ⇒   3 a - b = 7       … 1 Also f ' 4 3 = 0 (given) ⇒   3 x 2 - 2 a x + b x = 4 3 = 0 ⇒   16 3 - 8 a 3 + b = 0 ⇒   8 a - 3 b - 16 = 0             … 2 Solving 1 and 2 a = 5 ,   b = 8

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