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JEE Main20254 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

Let a 0 . If the function f ( x )=6 x ^3-45 a x ^2+108 a ^2 x +1 attains its local maximum and minimum values at the points x₁ and x₂ respectively such that x₁ x₂=54 , then a + x ₁+ x ₂ is equal to :-

Options

  1. A15
  2. B18
  3. C24
  4. D13

Correct answer

B. 18

Step-by-step solution

aligned & f^ (x)=18 x^2-90 a x+108 a^2=0 & x=2 a & x=3 a & x₁=2 a x₂=3 a & x₁ x₂=54 & 6 a^2=54 & a=3 & a+x₁+x₂ & 3+2 3+3 3=18 & option (2) aligned

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