Home
Class 12
MATHS
For what real values of a' and 'b' all t...

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`

Text Solution

Verified by Experts

The correct Answer is:
`if a= (-9)/(5) , " then " b gt (36)/(5) ; if a = (81)/(25) " then " b gt (400)/(243)`
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

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

Find the extreme values of the function y=2x^3-9x^2+12x+5

Find the maximum value of the function f(x)=5+9x-18x^(2)

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

The minimum value of the function f (x) =x^(3) -3x^(2) -9x+5 is :

Consider the function f(x)=0.75x^(4)-x^(3)-9x^(2)+7 What is the maximum value of the function ?

Find the values of a for which the function f(x)=(a+2)x^(3)-3ax^(2)+9ax-a decreasing for all real values of x.

Find the values 'a' for which the function f(x)=(a+2)x^(3)-3ax^(2)+9ax-1 decreases for all real values of x

RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. find the interval of increasing and decreasing for the function g...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find the cosine of the angle at the vertex of an isoceles triangl...

    Text Solution

    |

  9. A tangent to the curve y=1 -x^(3) is drawn so that the abscissa x(0)...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the minimum distance of origin from the curve ax^(2) +2bxy+ay^(2)...

    Text Solution

    |

  12. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

    Text Solution

    |

  13. Find which of the two larger en (1+x) " or " (tan^(-1)x)/(1+x).

    Text Solution

    |

  14. Let f'(sin x) lt 0 and f''(sin x) gt 0 AA x in (0, pi/2) and g (x) =...

    Text Solution

    |

  15. Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(...

    Text Solution

    |

  16. f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) su...

    Text Solution

    |

  17. Find all the values of the parameter'a' for which the function; f(x)=...

    Text Solution

    |

  18. Let h be a twice continuously differentiable positive function on an o...

    Text Solution

    |

  19. if the complete set of values (s) of 'a' for which the function f (x)...

    Text Solution

    |

  20. if two curves y=2 sin ((5pi)/6)x and y=alphax^(2)-3ax+2alpha+1 touch ...

    Text Solution

    |