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For a gt 0, if the function f(x)=2 x^(3...

For `a gt 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 =`

A

3

B

1

C

2

D

`1//2`

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-APPLICATIONS OF DIFFERENTIATION-EXERCISE 1E (MAXIMA AND MINIMA)
  1. The least value of f(x) = sin 2x -x on [-pi//2,pi//2] is

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  2. The difference between the greatest and least value of the function f(...

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  3. For a gt 0, if the function f(x)=2 x^(3) - 9 a x^(2) + 12 a^(2) x + 1...

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  4. If ma and M respectively denote the minimum and maximum of f(x) =(x-1)...

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  5. Let f : R to R be defined, by {{:(k-2x,"if"" "x le -1),(2x+3,"if" " "...

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  6. p and q are distinct prime numbers and if the equation x^2 -px ...

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  7. Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real ro...

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  8. A curve passes through the point (2,0) and the lope of the tangent at ...

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  9. The point on the curve y=x/(1+x^2) where the tangent to the curve has ...

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  10. The curve y=ax^2+bx has minimum at (2,-12) on it. Then (a,b) =

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  11. If f(x) = a/x +bx has minimum at (2,1) then (a,b) =

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  12. If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

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  13. If a quadratic function in x has the value 9 when x=1 and has maximum ...

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  14. A cubic function of x has maximum 10 and minimum -5/2, when x = -3 and...

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  15. The real number x when added to its inverse gives the minimum value of...

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  16. If the product of two positive numbers is 400 then the minimum value o...

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  17. The sum of two positive numbers is 12. The numbers so that the sum of ...

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  18. The difference of two positive numbers is 10 . If the square of the gr...

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  19. The sum of three numbers is 30 . The first plus three times the second...

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  20. Divide 64 into two parts such that the sum of the cubes of two parts i...

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