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AP EAMCET20227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The function f(x)=2 x^3-9 a x^2+12 a^2 x+1(a>0) attains its maximum and minimum at p and q respectively and p^2=q . Then, a=

Options

  1. A1
  2. B2
  3. C1 / 2
  4. D3

Correct answer

B. 2

Step-by-step solution

aligned & f(x)=2 x^3-9 a x^2+12 a^2 x+1, a>0 & f^ (x)=6 x^2-18 a x+12 a^2 aligned =6 (x^2-3 a x+2 a^2 )=6(x-a)(x-2 a) For maxima or minima f^ (x)=0 x=a, 2 a p=a and q=2 a According to question, p^2=q and a^2=2 a a(a-2)=0 a=0,2 a=2[ a>0]

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