If the function f ( x )=2 x ^2-9 a x ^2+12 a ^2 x +1 , where a 0 , attains its maximum and minimum at p and q respectively such that p ^2= q , then a equals

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If the function f ( x )=2 x ^2-9 a x ^2+12 a ^2 x +1 , where a >0 , attains its maximum and minimum at p and q respectively such that p ^2= q , then a equals

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Correct answer: D. 2

f(x)=2 x^3-9 a x^2+12 a^2 x+1f^ (x)=6 x^2-18 a x+12 a^2 ; f^ (x)=12 x-18 a For max. or min. 6 x^2-18 a x+12 a^2=0 x^2-3 a x+2 a^2=0 x = a or x =2 a , at x = a max.and at x =2 a . p^2=qa^2=2 a a=2 or a=0 but a >0 , therefore, a =2 .

If the function f ( x )=2 x ^2-9 a x ^2+12 a ^2 x +1 , where a >0 , attains its maximum and minimum at p and q respectively such that p ^2= q , then a equals

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