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 ENGLISH|Exercise Exersise-3 Part II|22 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

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

If the function f(x) = x^3 + 3(a-7)x^2 +3(a^2-9)x-1 has a positive point Maximum , then

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

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

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .

Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 for some value of x in [a , b]dot

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

The interval on which the function f(x) = 2x^(3) + 9x^(2) + 12 x - 1 is decreasing is

It is given that the Rolles' theorem holds for the function f(x)=x^3+b x^2+c x ,x in [1,2] at the point x=4/3dot Find the values of b and c

Let f(x) =x^(3)-3x +2. Examine the monotonicity of function at points x=0.1,2

RESONANCE ENGLISH-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. If the function f:[0,4]vecR is differentiable, the show that for a , b...

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

    Text Solution

    |

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

    Text Solution

    |

  9. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,\ -1) , find the val...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find the interval of increase and decrease for the function g(x) =...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. For any acute angled triangleABC,(sinA)/(A)+(sinB)/(B)+(sinC)/(C ) can

    Text Solution

    |

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

    Text Solution

    |

  18. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  19. The cosine of the angle at the vertex of an isosceles triangle having ...

    Text Solution

    |

  20. A cone is made from a circular sheet of radius sqrt3 by cutting out a ...

    Text Solution

    |