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AP EAMCET201921 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

For a>0 , if the function f(x)=2 x^3-9 a x^2+12 a^2 x+1 attains its maximum value at p and minimum value at q such that p^2=q , then a=

Options

  1. A1 2
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Given, f(x)=2 x^3-9 a x^2+12 a^2 x+1 has maximum value at P and minimum value at q . So, f^ (p)=0 and f^ (q)=0 Now, f^ (x)=6 x^2-18 a x+12 a^2 has roots p and q aligned & & p+q & = 18 a 6 =3 a & and & p q & = 12 a^2 6 =2 a^2 aligned on solving both equations, we get aligned & p=a and q=2 a & Given, & p^2=q & a^2=2 a & a^2-2 a=0 & a(a-2)=0 & a=2 ( a 0) & aligned

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