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JEE Main20202 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

If p x be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2 then p 0 is equal to

Options

  1. A6
  2. B- 12
  3. C24
  4. D12

Correct answer

B. - 12

Step-by-step solution

Clearly p ' ( x ) = λ ( x - 1 ) ( x - 2 ) where λ > 0 Integrating both sides p x = λ x 3 3 - 3 x 2 2 + 2 x + C Given p 1 = 8 ⇒ λ 1 3 - 3 2 + 2 + C = 8    ⇒ 5 λ 6 + C = 8     . . . 1 p ( 2 ) = 4 ⇒ λ 8 3 - 6 + 4 + C = 4    ⇒ 2 3 λ + C = 4     . . . 2 By 1 and 2 ⇒ C = - 12 ⇒ p ( 0 ) = - 12

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