Home
Class 12
MATHS
if all the function f(x)=a^2x^3-a/9x^2-2...

if all the function `f(x)=a^2x^3-a/9x^2-2x-b` arepositive and the minimum is at the point x = 1/3 , then show that when a= -2 , b< -11/27 and when a=3, b< -1/2

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

if all the function f(x)=a^(2)x^(3)-(a)/(9)x^(2)-2x-b arepositive and the minimum is at the point x=1/3, then show that when a=-2,b<-11/27 and when a=3,b<-1/2

The values of a and b for which all the extrema of the function, f(x)=a^(2)x^(3)-0.5ax^(2)-2x-b, is positive and the minima is at the point x_(0)=(1)/(3), are

The function f(x)=2x^3-3x^2-12x+5 has a minimum at x=

For what real values of a' and 'b' all the extrema of the function f(x)=(5a^(2))/(3)x^(3)+2ax^(2)-9x+b are positive and the maximum is at the point x_(0)=-(5)/(9)

The function f(x)=2x^3+9x^2+12x+20 is increasing in the interval

The function f (x) = (2-x)/(9x-x^(3)) is:

f(x)=2x^(3)-3x^(2)-12x+12 has minimum at the point

The function f(x)=2x^(3)-3(a+b)x^(2)+6abx has a local maximum at x=a , if

f(x)=2x^(3)-9x^(2)+12x+5 has maximum at the point

RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

    Text Solution

    |

  2. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

    Text Solution

    |

  3. if all the function f(x)=a^2x^3-a/9x^2-2x-b arepositive and the minimu...

    Text Solution

    |

  4. if f(x) = {underset(a^(2) -2+ (sin (x-K))/(x-K))(3+|x-k|)," "underse...

    Text Solution

    |

  5. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

    Text Solution

    |

  6. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

    Text Solution

    |

  7. Consider the equation x^4+4x^3-8x^2+K=0. Answer the following (1) Th...

    Text Solution

    |

  8. A function f(x) having the following properties, (i) f(x) is conti...

    Text Solution

    |

  9. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  10. If y=(a x+b)/((x-1)(x-4)) has a turning value at (2,\ -1) find a\ &...

    Text Solution

    |

  11. if A be the area of a triangle, prove that the error in A resulting fr...

    Text Solution

    |

  12. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

    Text Solution

    |

  13. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  14. find the interval of increasing and decreasing for the function g...

    Text Solution

    |

  15. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  16. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  17. For any acute angled DeltaABC find the maximum value of (sin A)/(A) +(...

    Text Solution

    |

  18. For what real values of a' and 'b' all the extrema of the function f(x...

    Text Solution

    |

  19. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  20. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |