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JEE Main20252 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

If the function f(x)=2 x^3-9 ax ^2+12 a ^2 x +1 , where a 0 , attains its local maximum and local minimum values at p and q , respectively, such that p ^2= q , then f(3) is equal to:

Options

  1. A55
  2. B10
  3. C23
  4. D37

Correct answer

D. 37

Step-by-step solution

f^ (x)=6 x^2-18 a x+12 a^2 f^ (x)=6 (x^2-3 a x+2 a^2 ) roots are a, 2 a p ^2= q a ^2=2 a a=2 f(x)=2 x^3-18 x^2+48 x+1 f(3)=37

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