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JEE Main20198 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

If S 1 and S 2 are respectively the sets of local minimum and local maximum points of the function, f x = 9 x 4 + 12 x 3 - 36 x 2 + 25 , x ∈ R , then

Options

  1. AS 1 = - 2 ; S 2 = 0,1
  2. BS 1 = - 1 ; S 2 = 0,2
  3. CS 1 = - 2,0 ; S 2 = 1
  4. DS 1 = - 2,1 ; S 2 = 0

Correct answer

D. S 1 = - 2,1 ; S 2 = 0

Step-by-step solution

y = 9 x 4 + 12 x 3 - 36 x 2 + 25 Differentiating, d y d x = 36 x 3 + 36 x 2 - 72 x = 36 x x 2 + x - 2 = 36 x x + 2 x - 1 Sign convention for d y d x ∴ S 1 = - 2,1 &   S 2 = 0

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