Home
Class 12
MATHS
If the function f(x)=2x^3-9ax^2+12a^2x+1...

If the function `f(x)=2x^3-9ax^2+12a^2x+1,` where `a gt 0,` attains its maximum and minimum at `p and q,` respectively, such that `p^2=q,` then `a` equal to (a) `1` (b) `2` (c) `1/2` (d) `3`

A

0

B

1

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q , respectively, then (p , q)= (a) (0,1) (b) (1,3) (c) (1,0) (d) none of these

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

The function 'f' is defined by f(x)=x^p(1-x)^q for all x\ in R , where p ,\ q are positive integers, has a maximum value, for x equal to : (p q)/(p+q) (b) 1 (c) 0 (d) p/(p+q)

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

suppose x_1, and x_2 are the point of maximum and the point of minimum respectively of the function f(x)=2x^3-9ax^2 + 12a^2x + 1 respectively, (a> o) then for the equality x_1^2 = x_2 to be true the value of 'a' must be

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1

If f : R->Q (Rational numbers), g : R ->Q (Rational numbers) are two continuous functions such that sqrt(3)f(x)+g(x)=4 then (1-f(x))^3+(g(x)-3)^3 is equal to (1) 1 (2) 2 (3) 3 (4) 4

OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Exercise
  1. If the function f(x) = x^3 + 3(a-7)x^2 +3(a^2-9)x-1 has a positive ...

    Text Solution

    |

  2. Show that the maximum value of (1/x)^x is e^(1/e)dot

    Text Solution

    |

  3. If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...

    Text Solution

    |

  4. The maximum distance of the point (k,0) from the curve 2x^(2) +y^(2)...

    Text Solution

    |

  5. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

    Text Solution

    |

  6. An isosceles triangle of vertical angle 2theta is inscribed in a ...

    Text Solution

    |

  7. Find minimum value of px+qy where p>0, q>0, x>0, y>0 when xy=r,^2 with...

    Text Solution

    |

  8. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

    Text Solution

    |

  9. If (x+c)/(1+x^2) where c is a constant , then when y is stationary , x...

    Text Solution

    |

  10. N Characters of information are held on magnetic tape, in batches of x...

    Text Solution

    |

  11. Statement I If A gt 0 , B gt 0 and A+B= pi/3, then the maximum value o...

    Text Solution

    |

  12. The largest value of 2x^(3)-3x^(2)-12x+5 for -2 le x le 2 occurs when

    Text Solution

    |

  13. The first and second order derivatives of a function f(x) exit at all ...

    Text Solution

    |

  14. The minimum value of 2^(x^2-3)^(3) +27 is 2^(27) (b) 2 (c) 1 (d) ...

    Text Solution

    |

  15. Let f(x) =cosx sin2x. Then , min (f(x):-pilexlepi) is

    Text Solution

    |

  16. If f(x)=sin^6x+cos^6x , then which one of the following is false

    Text Solution

    |

  17. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

    Text Solution

    |

  18. If ax+b/x >= c for all positive x, where a, b, c > 0, then-

    Text Solution

    |

  19. The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...

    Text Solution

    |

  20. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

    Text Solution

    |